Daily Papers

This article introduces Regression Discontinuity Design (RDD) with Distribution-Valued Outcomes (R3D), extending the standard RDD framework to settings where the outcome is a distribution rather than a scalar. Such settings arise when treatment is assigned at a higher level of aggregation than the outcome-for example, when a subsidy is allocated based on a firm-level revenue cutoff while the outcome of interest is the distribution of employee wages within the firm. Since standard RDD methods cannot accommodate such two-level randomness, I propose a novel approach based on random distributions. The target estimand is a "local average quantile treatment effect", which averages across random quantiles. To estimate this target, I introduce two related approaches: one that extends local polynomial regression to random quantiles and another based on local Fr\'echet regression, a form of functional regression. For both estimators, I establish asymptotic normality and develop uniform, debiased confidence bands together with a data-driven bandwidth selection procedure. Simulations validate these theoretical properties and show existing methods to be biased and inconsistent in this setting. I then apply the proposed methods to study the effects of gubernatorial party control on within-state income distributions in the US, using a close-election design. The results suggest a classic equality-efficiency tradeoff under Democratic governorship, driven by reductions in income at the top of the distribution.

Large Language Models (LLMs) are often trained on vast amounts of undisclosed data, motivating the development of post-hoc Membership Inference Attacks (MIAs) to gain insight into their training data composition. However, in this paper, we identify inherent challenges in post-hoc MIA evaluation due to potential distribution shifts between collected member and non-member datasets. Using a simple bag-of-words classifier, we demonstrate that datasets used in recent post-hoc MIAs suffer from significant distribution shifts, in some cases achieving near-perfect distinction between members and non-members. This implies that previously reported high MIA performance may be largely attributable to these shifts rather than model memorization. We confirm that randomized, controlled setups eliminate such shifts and thus enable the development and fair evaluation of new MIAs. However, we note that such randomized setups are rarely available for the latest LLMs, making post-hoc data collection still required to infer membership for real-world LLMs. As a potential solution, we propose a Regression Discontinuity Design (RDD) approach for post-hoc data collection, which substantially mitigates distribution shifts. Evaluating various MIA methods on this RDD setup yields performance barely above random guessing, in stark contrast to previously reported results. Overall, our findings highlight the challenges in accurately measuring LLM memorization and the need for careful experimental design in (post-hoc) membership inference tasks.

Sharp, multidimensional changepoints-abrupt shifts in a regression surface whose locations and magnitudes are unknown-arise in settings as varied as gene-expression profiling, financial covariance breaks, climate-regime detection, and urban socioeconomic mapping. Despite their prevalence, there are no current approaches that jointly estimate the location and size of the discontinuity set in a one-shot approach with statistical guarantees. We therefore introduce Free Discontinuity Regression (FDR), a fully nonparametric estimator that simultaneously (i) smooths a regression surface, (ii) segments it into contiguous regions, and (iii) provably recovers the precise locations and sizes of its jumps. By extending a convex relaxation of the Mumford-Shah functional to random spatial sampling and correlated noise, FDR overcomes the fixed-grid and i.i.d. noise assumptions of classical image-segmentation approaches, thus enabling its application to real-world data of any dimension. This yields the first identification and uniform consistency results for multivariate jump surfaces: under mild SBV regularity, the estimated function, its discontinuity set, and all jump sizes converge to their true population counterparts. Hyperparameters are selected automatically from the data using Stein's Unbiased Risk Estimate, and large-scale simulations up to three dimensions validate the theoretical results and demonstrate good finite-sample performance. Applying FDR to an internet shutdown in India reveals a 25-35% reduction in economic activity around the estimated shutdown boundaries-much larger than previous estimates. By unifying smoothing, segmentation, and effect-size recovery in a general statistical setting, FDR turns free-discontinuity ideas into a practical tool with formal guarantees for modern multivariate data.

Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for jumps in conditional means when outcomes lie in a non-Euclidean metric space. Using local Fr\'echet regressionx2014which generalizes standard regression to metric-space valued datax2014the method estimates a mean path on either side of a candidate cutoff, extending existing k-sample tests to a flexible regression setting. Key theoretical contributions include a central limit theorem for the local estimator of the conditional Fr\'echet variance and the asymptotic validity and consistency of the proposed test. Simulations confirm nominal size control and robust power in finite samples. Two applications demonstrate the method's value by revealing effects invisible to scalar-based tests. First, I detect a sharp change in work-from-home compositions at Washington State's income threshold for non-compete enforceability during COVID-19, highlighting remote work's role as a bargaining margin. Second, I find that countries restructure their input-output networks after losing preferential US trade access. These findings underscore that analyzing regression functions within their native metric spaces can reveal structural discontinuities that scalar summaries would miss.

In policy gradient reinforcement learning, access to a differentiable model enables 1st-order gradient estimation that accelerates learning compared to relying solely on derivative-free 0th-order estimators. However, discontinuous dynamics cause bias and undermine the effectiveness of 1st-order estimators. Prior work addressed this bias by constructing a confidence interval around the REINFORCE 0th-order gradient estimator and using these bounds to detect discontinuities. However, the REINFORCE estimator is notoriously noisy, and we find that this method requires task-specific hyperparameter tuning and has low sample efficiency. This paper asks whether such bias is the primary obstacle and what minimal fixes suffice. First, we re-examine standard discontinuous settings from prior work and introduce DDCG, a lightweight test that switches estimators in nonsmooth regions; with a single hyperparameter, DDCG achieves robust performance and remains reliable with small samples. Second, on differentiable robotics control tasks, we present IVW-H, a per-step inverse-variance implementation that stabilizes variance without explicit discontinuity detection and yields strong results. Together, these findings indicate that while estimator switching improves robustness in controlled studies, careful variance control often dominates in practical deployments.

Neural scaling laws approximate a language model's loss as a power-law function of parameter count N and token count D. Following Chinchilla-style compute-optimal training, many studies fit scaling laws from runs performed under a fixed tokens-per-parameter (TPP) ratio k and set D = kN. We show that this collinear design, combined with the empirically common near-equality of the exponents governing N and D, induces an inherent ill-conditioning in the Gauss-Newton least-squares problem: the condition number of the design grows as the inverse square of the gap between the N and D-exponents. The scale coefficients become practically unidentifiable, with confidence intervals inflating by an order of magnitude or more, yielding a ``sloppy'' model whose extrapolations degrade sharply off the training ray. We prove this for four scaling-law formalisms and derive a closed-form TPP-diversity threshold that is necessary and sufficient for well-conditioned estimation. Empirically, non-collinear designs outperform collinear ones on held-out splits with a 97.3\% win rate across four laws, five corpora, multiple floating point precision modes. We further show the degeneracy is rooted in Jacobian geometry and is not an artifact of the loss function: any smooth estimation objective whose curvature involves the Jacobian inherits the same ill-conditioning.

Probabilistic models are typically trained using task-agnostic objectives like log-loss, which can lead to significant errors in downstream estimation. This disconnect is especially critical in Inverse Probability Weighting (IPW) for causal inference, where propensity score errors near 0 and 1 often lead to high bias and variance. We propose a principled framework for deriving task-specific strictly proper scoring rules by matching the local curvature of the downstream error metric. We apply this to the Average Treatment Effect (ATE) estimation, deriving a closed-form loss and its corresponding canonical probability mapping that can be readily integrated with any model like a neural network or a gradient boosting algorithm. Extensive evaluations on causal inference benchmarks demonstrate that our tailored objective consistently outperforms standard likelihood-based and covariate-balancing approaches.

The push for efficient text to image synthesis has moved the field toward one step sampling, yet existing methods still face a three way tradeoff among fidelity, inference speed, and training efficiency. Approaches that rely on external discriminators can sharpen one step performance, but they often introduce training instability, high GPU memory overhead, and slow convergence, which complicates scaling and parameter efficient tuning. In contrast, regression based distillation and consistency objectives are easier to optimize, but they typically lose fine details when constrained to a single step. We present APEX, built on a key theoretical insight: adversarial correction signals can be extracted endogenously from a flow model through condition shifting. Using a transformation creates a shifted condition branch whose velocity field serves as an independent estimator of the model's current generation distribution, yielding a gradient that is provably GAN aligned, replacing the sample dependent discriminator terms that cause gradient vanishing. This discriminator free design is architecture preserving, making APEX a plug and play framework compatible with both full parameter and LoRA based tuning. Empirically, our 0.6B model surpasses FLUX-Schnell 12B (20times more parameters) in one step quality. With LoRA tuning on Qwen-Image 20B, APEX reaches a GenEval score of 0.89 at NFE=1 in 6 hours, surpassing the original 50-step teacher (0.87) and providing a 15.33times inference speedup. Code is available https://github.com/LINs-lab/APEX.

In our era of enormous neural networks, empirical progress has been driven by the philosophy that more is better. Recent deep learning practice has found repeatedly that larger model size, more data, and more computation (resulting in lower training loss) improves performance. In this paper, we give theoretical backing to these empirical observations by showing that these three properties hold in random feature (RF) regression, a class of models equivalent to shallow networks with only the last layer trained. Concretely, we first show that the test risk of RF regression decreases monotonically with both the number of features and the number of samples, provided the ridge penalty is tuned optimally. In particular, this implies that infinite width RF architectures are preferable to those of any finite width. We then proceed to demonstrate that, for a large class of tasks characterized by powerlaw eigenstructure, training to near-zero training loss is obligatory: near-optimal performance can only be achieved when the training error is much smaller than the test error. Grounding our theory in real-world data, we find empirically that standard computer vision tasks with convolutional neural tangent kernels clearly fall into this class. Taken together, our results tell a simple, testable story of the benefits of overparameterization, overfitting, and more data in random feature models.

Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the system state will evolve over time, and the design challenge is to optimize the initial conditions that lead to a target outcome. Recent developments in learned simulation have shown that graph neural networks (GNNs) can be used for accurate, efficient, differentiable estimation of simulator dynamics, and support high-quality design optimization with gradient- or sampling-based optimization procedures. However, optimizing designs from scratch requires many expensive model queries, and these procedures exhibit basic failures on either non-convex or high-dimensional problems.In this work, we show how denoising diffusion models (DDMs) can be used to solve inverse design problems efficiently and propose a particle sampling algorithm for further improving their efficiency. We perform experiments on a number of fluid dynamics design challenges, and find that our approach substantially reduces the number of calls to the simulator compared to standard techniques.

Conformal prediction (CP) for regression can be challenging, especially when the output distribution is heteroscedastic, multimodal, or skewed. Some of the issues can be addressed by estimating a distribution over the output, but in reality, such approaches can be sensitive to estimation error and yield unstable intervals.~Here, we circumvent the challenges by converting regression to a classification problem and then use CP for classification to obtain CP sets for regression.~To preserve the ordering of the continuous-output space, we design a new loss function and make necessary modifications to the CP classification techniques.~Empirical results on many benchmarks shows that this simple approach gives surprisingly good results on many practical problems.

In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding with a polyharmonic spline. However, a direct application of that solution is limited by O(N^3) computational cost and by a breakdown of the original theoretical assumptions when the input space has excessive dimensionality. This paper proposes a cascade architecture built from packages of polyharmonic splines that simultaneously addresses scalability and is theoretically justified for problems with unknown intrinsic low dimensionality. Efficient matrix procedures are presented for forward computation and end-to-end differentiation through the cascade.

The presence of distribution shifts poses a significant challenge for deploying modern machine learning models in real-world applications. This work focuses on the target shift problem in a regression setting (Zhang et al., 2013; Nguyen et al., 2016). More specifically, the target variable y (also known as the response variable), which is continuous, has different marginal distributions in the training source and testing domain, while the conditional distribution of features x given y remains the same. While most literature focuses on classification tasks with finite target space, the regression problem has an infinite dimensional target space, which makes many of the existing methods inapplicable. In this work, we show that the continuous target shift problem can be addressed by estimating the importance weight function from an ill-posed integral equation. We propose a nonparametric regularized approach named ReTaSA to solve the ill-posed integral equation and provide theoretical justification for the estimated importance weight function. The effectiveness of the proposed method has been demonstrated with extensive numerical studies on synthetic and real-world datasets.

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

Behavior of deep neural networks can be inconsistent between different versions. Regressions during model update are a common cause of concern that often over-weigh the benefits in accuracy or efficiency gain. This work focuses on quantifying, reducing and analyzing regression errors in the NLP model updates. Using negative flip rate as regression measure, we show that regression has a prevalent presence across tasks in the GLUE benchmark. We formulate the regression-free model updates into a constrained optimization problem, and further reduce it into a relaxed form which can be approximately optimized through knowledge distillation training method. We empirically analyze how model ensemble reduces regression. Finally, we conduct CheckList behavioral testing to understand the distribution of regressions across linguistic phenomena, and the efficacy of ensemble and distillation methods.

Proximal causal learning is a promising framework for identifying the causal effect under the existence of unmeasured confounders. Within this framework, the doubly robust (DR) estimator was derived and has shown its effectiveness in estimation, especially when the model assumption is violated. However, the current form of the DR estimator is restricted to binary treatments, while the treatment can be continuous in many real-world applications. The primary obstacle to continuous treatments resides in the delta function present in the original DR estimator, making it infeasible in causal effect estimation and introducing a heavy computational burden in nuisance function estimation. To address these challenges, we propose a kernel-based DR estimator that can well handle continuous treatments. Equipped with its smoothness, we show that its oracle form is a consistent approximation of the influence function. Further, we propose a new approach to efficiently solve the nuisance functions. We then provide a comprehensive convergence analysis in terms of the mean square error. We demonstrate the utility of our estimator on synthetic datasets and real-world applications.

The technique of data augmentation (DA) is often used in machine learning for regularization purposes to better generalize under i.i.d. settings. In this work, we present a unifying framework with topics in causal inference to make a case for the use of DA beyond just the i.i.d. setting, but for generalization across interventions as well. Specifically, we argue that when the outcome generating mechanism is invariant to our choice of DA, then such augmentations can effectively be thought of as interventions on the treatment generating mechanism itself. This can potentially help to reduce bias in causal effect estimation arising from hidden confounders. In the presence of such unobserved confounding we typically make use of instrumental variables (IVs) -- sources of treatment randomization that are conditionally independent of the outcome. However, IVs may not be as readily available as DA for many applications, which is the main motivation behind this work. By appropriately regularizing IV based estimators, we introduce the concept of IV-like (IVL) regression for mitigating confounding bias and improving predictive performance across interventions even when certain IV properties are relaxed. Finally, we cast parameterized DA as an IVL regression problem and show that when used in composition can simulate a worst-case application of such DA, further improving performance on causal estimation and generalization tasks beyond what simple DA may offer. This is shown both theoretically for the population case and via simulation experiments for the finite sample case using a simple linear example. We also present real data experiments to support our case.

Autonomous scientific discovery systems offer the potential to accelerate research by automating the process of hypothesis generation and validation. However, current systems operate within constrained search spaces or require predefined research questions, limiting their capacity for true open-ended inquiry. Furthermore, while they generate hypotheses iteratively, they largely lack the ability to explicitly synthesize their own accumulated findings to uncover complex, interconnected phenomena. We introduce DiscoPER, an autonomous large language model-powered framework that conducts open-ended research by dynamically generating and executing code to explore datasets without pre-specified research objectives. To ensure rigorous scientific validity, every proposed discovery must pass statistical testing. To overcome the limitations of isolated search, our framework introduces a second-order reasoning mechanism that periodically analyzes its own accumulated discoveries. By treating prior discoveries as empirical data, DiscoPER identifies structural patterns, confounds, and epistemic gaps, actively redirecting hypothesis exploration toward uncharted regions of the search space. The search space is further expanded by incorporating tool use, enabling the system to explore hypotheses beyond structured metadata by seamlessly processing and extracting useful information from multimodal sources like images. Evaluated on iNatDisco, a new multimodal ecological knowledge benchmark with pattern-level ground truth obtained from peer-reviewed literature, DiscoPER recovers 8 of 9 known patterns with a 72.7% hypothesis support rate, outperforming both classical causal discovery and LLM-guided baselines. Ablations show that DiscoPER scales with more data, and confirms the benefits of second-order meta-reflection.

Traditional direct estimation methods are not efficient for domains of a survey population with small sample sizes. To estimate the domain proportions, we combine the direct estimators and the regression-synthetic estimators based on domain-level auxiliary information. For the case of small true proportions, we introduce the design-based linear combination that is a robust alternative to the empirical best linear unbiased predictor (EBLUP) based on the Fay--Herriot model. We also consider an adaptive procedure optimizing a sample-size-dependent composite estimator, which depends on a single parameter for all domains. We imitate the Lithuanian Labor Force Survey, where we estimate the proportions of the unemployed and employed in municipalities. We show where the considered design-based compositions and estimators of their mean square errors are competitive for EBLUP and its accuracy estimation.

We introduce Multi-Objective Counterfactuals for Design (MCD), a novel method for counterfactual optimization in design problems. Counterfactuals are hypothetical situations that can lead to a different decision or choice. In this paper, the authors frame the counterfactual search problem as a design recommendation tool that can help identify modifications to a design, leading to better functional performance. MCD improves upon existing counterfactual search methods by supporting multi-objective queries, which are crucial in design problems, and by decoupling the counterfactual search and sampling processes, thus enhancing efficiency and facilitating objective tradeoff visualization. The paper demonstrates MCD's core functionality using a two-dimensional test case, followed by three case studies of bicycle design that showcase MCD's effectiveness in real-world design problems. In the first case study, MCD excels at recommending modifications to query designs that can significantly enhance functional performance, such as weight savings and improvements to the structural safety factor. The second case study demonstrates that MCD can work with a pre-trained language model to suggest design changes based on a subjective text prompt effectively. Lastly, the authors task MCD with increasing a query design's similarity to a target image and text prompt while simultaneously reducing weight and improving structural performance, demonstrating MCD's performance on a complex multimodal query. Overall, MCD has the potential to provide valuable recommendations for practitioners and design automation researchers looking for answers to their ``What if'' questions by exploring hypothetical design modifications and their impact on multiple design objectives. The code, test problems, and datasets used in the paper are available to the public at decode.mit.edu/projects/counterfactuals/.

Answering counterfactual queries has many important applications such as knowledge discovery and explainability, but is challenging when causal variables are unobserved and we only see a projection onto an observation space, for instance, image pixels. One approach is to recover the latent Structural Causal Model (SCM), but this typically needs unrealistic assumptions, such as linearity of the causal mechanisms. Another approach is to use na\"ive ML approximations, such as generative models, to generate counterfactual samples; however, these lack guarantees of accuracy. In this work, we strive to strike a balance between practicality and theoretical guarantees by focusing on a specific type of causal query called domain counterfactuals, which hypothesizes what a sample would have looked like if it had been generated in a different domain (or environment). Concretely, by only assuming invertibility, sparse domain interventions and access to observational data from different domains, we aim to improve domain counterfactual estimation both theoretically and practically with less restrictive assumptions. We define domain counterfactually equivalent models and prove necessary and sufficient properties for equivalent models that provide a tight characterization of the domain counterfactual equivalence classes. Building upon this result, we prove that every equivalence class contains a model where all intervened variables are at the end when topologically sorted by the causal DAG. This surprising result suggests that a model design that only allows intervention in the last k latent variables may improve model estimation for counterfactuals. We then test this model design on extensive simulated and image-based experiments which show the sparse canonical model indeed improves counterfactual estimation over baseline non-sparse models.

Off-policy actor-critic methods in reinforcement learning train a critic with temporal-difference updates and use it as a learning signal for the policy (actor). This design typically achieves higher sample efficiency than purely on-policy methods. However, critic networks tend to overestimate value estimates systematically. This is often addressed by introducing a pessimistic bias based on uncertainty estimates. Current methods employ ensembling to quantify the critic's epistemic uncertainty-uncertainty due to limited data and model ambiguity-to scale pessimistic updates. In this work, we propose a new algorithm called Stochastic Actor-Critic (STAC) that incorporates temporal (one-step) aleatoric uncertainty-uncertainty arising from stochastic transitions, rewards, and policy-induced variability in Bellman targets-to scale pessimistic bias in temporal-difference updates, rather than relying on epistemic uncertainty. STAC uses a single distributional critic network to model the temporal return uncertainty, and applies dropout to both the critic and actor networks for regularization. Our results show that pessimism based on a distributional critic alone suffices to mitigate overestimation, and naturally leads to risk-averse behavior in stochastic environments. Introducing dropout further improves training stability and performance by means of regularization. With this design, STAC achieves improved computational efficiency using a single distributional critic network.

Large language models are being widely used across industries to generate content that contributes directly to key performance metrics, such as conversion rates. Pretrained models, however, often fall short when it comes to aligning with human preferences or optimizing for business objectives. As a result, fine-tuning with good-quality labeled data is essential to guide models to generate content that achieves better results. Controlled experiments, like A/B tests, can provide such data, but they are often expensive and come with significant engineering and logistical challenges. Meanwhile, companies have access to a vast amount of historical (observational) data that remains underutilized. In this work, we study the challenges and opportunities of fine-tuning LLMs using observational data. We show that while observational outcomes can provide valuable supervision, directly fine-tuning models on such data can lead them to learn spurious correlations. We present empirical evidence of this issue using various real-world datasets and propose DeconfoundLM, a method that explicitly removes the effect of known confounders from reward signals. Using simulation experiments, we demonstrate that DeconfoundLM improves the recovery of causal relationships and mitigates failure modes found in fine-tuning methods that ignore or naively incorporate confounding variables. Our findings highlight that while observational data presents risks, with the right causal corrections, it can be a powerful source of signal for LLM alignment. Please refer to the project page for code and related resources.

Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We first show that the marginal coverage guarantee of conformal prediction holds on imputed data for any missingness distribution and almost all imputation functions. However, we emphasize that the average coverage varies depending on the pattern of missing values: conformal methods tend to construct prediction intervals that under-cover the response conditionally to some missing patterns. This motivates our novel generalized conformalized quantile regression framework, missing data augmentation, which yields prediction intervals that are valid conditionally to the patterns of missing values, despite their exponential number. We then show that a universally consistent quantile regression algorithm trained on the imputed data is Bayes optimal for the pinball risk, thus achieving valid coverage conditionally to any given data point. Moreover, we examine the case of a linear model, which demonstrates the importance of our proposal in overcoming the heteroskedasticity induced by missing values. Using synthetic and data from critical care, we corroborate our theory and report improved performance of our methods.

Many political science theories relate to latent variables, but such quantities cannot be observed directly and must instead be estimated from data with inherent uncertainty. In regression models, when a variable is measured with error, its slope coefficient is known to be biased toward zero. We show how measurement error interacts with unique aspects of latent variable estimation, identification restrictions in particular, and demonstrate how common error adjustment strategies can worsen bias. We introduce a method for adjusting coefficients on latent predictors, which reduces bias and typically increases the magnitude of estimated coefficients, often dramatically. We illustrate these dynamics using several different estimation strategies for the latent predictors. Corrected estimates using our proposed method show stronger relationships -- sometimes up to 50% larger -- than those from naive regression. Our findings highlight the importance of considering measurement error in latent predictors and the inadequacy of many commonly used approaches for dealing with this issue.

Offline reinforcement learning (RL), where the agent aims to learn the optimal policy based on the data collected by a behavior policy, has attracted increasing attention in recent years. While offline RL with linear function approximation has been extensively studied with optimal results achieved under certain assumptions, many works shift their interest to offline RL with non-linear function approximation. However, limited works on offline RL with non-linear function approximation have instance-dependent regret guarantees. In this paper, we propose an oracle-efficient algorithm, dubbed Pessimistic Nonlinear Least-Square Value Iteration (PNLSVI), for offline RL with non-linear function approximation. Our algorithmic design comprises three innovative components: (1) a variance-based weighted regression scheme that can be applied to a wide range of function classes, (2) a subroutine for variance estimation, and (3) a planning phase that utilizes a pessimistic value iteration approach. Our algorithm enjoys a regret bound that has a tight dependency on the function class complexity and achieves minimax optimal instance-dependent regret when specialized to linear function approximation. Our work extends the previous instance-dependent results within simpler function classes, such as linear and differentiable function to a more general framework.

Overparametrization often helps improve the generalization performance. This paper proposes a dual view of overparametrization suggesting that downsampling may also help generalize. Motivated by this dual view, we characterize two out-of-sample prediction risks of the sketched ridgeless least square estimator in the proportional regime masymp n asymp p, where m is the sketching size, n the sample size, and p the feature dimensionality. Our results reveal the statistical role of downsampling. Specifically, downsampling does not always hurt the generalization performance, and may actually help improve it in some cases. We identify the optimal sketching sizes that minimize the out-of-sample prediction risks, and find that the optimally sketched estimator has stabler risk curves that eliminates the peaks of those for the full-sample estimator. We then propose a practical procedure to empirically identify the optimal sketching size. Finally, we extend our results to cover central limit theorems and misspecified models. Numerical studies strongly support our theory.

Evaluating modern machine learning models has become prohibitively expensive. Benchmarks such as LMMs-Eval and HELM demand thousands of GPU hours per model. Costly evaluation reduces inclusivity, slows the cycle of innovation, and worsens environmental impact. The typical approach follows two steps. First, select an anchor subset of data. Second, train a mapping from the accuracy on this subset to the final test result. The drawback is that anchor selection depends on clustering, which can be complex and sensitive to design choices. We argue that promoting diversity among samples is not essential; what matters is to select samples that maximise diversity in model responses. Our method, Diversifying Sample Condensation (DISCO), selects the top-k samples with the greatest model disagreements. This uses greedy, sample-wise statistics rather than global clustering. The approach is conceptually simpler. From a theoretical view, inter-model disagreement provides an information-theoretically optimal rule for such greedy selection. DISCO shows empirical gains over prior methods, achieving state-of-the-art results in performance prediction across MMLU, Hellaswag, Winogrande, and ARC. Code is available here: https://github.com/arubique/disco-public.

Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory. We consider here the classic regression setup, where a real valued square integrable r.v. Y is to be predicted upon observing a (possibly high dimensional) random vector X by means of a predictive function f(X) as accurately as possible in the mean-squared sense and study a nearest-neighbour-based pointwise estimate of the gradient of the optimal predictive function, the regression function m(x)=E[Ymid X=x]. Under classic smoothness conditions combined with the assumption that the tails of Y-m(X) are sub-Gaussian, we prove nonasymptotic bounds improving upon those obtained for alternative estimation methods. Beyond the novel theoretical results established, several illustrative numerical experiments have been carried out. The latter provide strong empirical evidence that the estimation method proposed works very well for various statistical problems involving gradient estimation, namely dimensionality reduction, stochastic gradient descent optimization and quantifying disentanglement.

Observational studies of causal effects require adjustment for confounding factors. In the tabular setting, where these factors are well-defined, separate random variables, the effect of confounding is well understood. However, in public policy, ecology, and in medicine, decisions are often made in non-tabular settings, informed by patterns or objects detected in images (e.g., maps, satellite or tomography imagery). Using such imagery for causal inference presents an opportunity because objects in the image may be related to the treatment and outcome of interest. In these cases, we rely on the images to adjust for confounding but observed data do not directly label the existence of the important objects. Motivated by real-world applications, we formalize this challenge, how it can be handled, and what conditions are sufficient to identify and estimate causal effects. We analyze finite-sample performance using simulation experiments, estimating effects using a propensity adjustment algorithm that employs a machine learning model to estimate the image confounding. Our experiments also examine sensitivity to misspecification of the image pattern mechanism. Finally, we use our methodology to estimate the effects of policy interventions on poverty in African communities from satellite imagery.

Learning to denoise has emerged as a prominent paradigm to design state-of-the-art deep generative models for natural images. How to use it to model the distributions of both continuous real-valued data and categorical data has been well studied in recently proposed diffusion models. However, it is found in this paper to have limited ability in modeling some other types of data, such as count and non-negative continuous data, that are often highly sparse, skewed, heavy-tailed, and/or overdispersed. To this end, we propose learning to jump as a general recipe for generative modeling of various types of data. Using a forward count thinning process to construct learning objectives to train a deep neural network, it employs a reverse count thickening process to iteratively refine its generation through that network. We demonstrate when learning to jump is expected to perform comparably to learning to denoise, and when it is expected to perform better. For example, learning to jump is recommended when the training data is non-negative and exhibits strong sparsity, skewness, heavy-tailedness, and/or heterogeneity.

Blind image quality assessment (BIQA) is commonly built on two basic learning paradigms: regression and ranking. Regression calibrates absolute scores, whereas ranking recovers quality structure from ordinal relations. Although joint regression-ranking supervision often improves BIQA, the relation between the two paradigms remains largely empirical and underexplored. In this work, we revisit what underlies regression and ranking and identify pairwise relational distance, termed quality margin, as their common bridge. Our derivation shows that, at the objective-optimization level, both paradigms fit quality margins: regression fits margins induced by score endpoints, while ranking fits transformed or sign-level margins through preference probabilities. Motivated by this insight, we propose MR-IQA, a direct quality-margin optimization framework for reinforcement learning (RL)-based BIQA. MR-IQA samples quality scores and optimizes pairwise margin errors as policy rewards, thereby modeling quality structure more explicitly. Experiments on six BIQA benchmarks show competitive general performance, and controlled comparisons demonstrate that MR-IQA achieves the strongest average PLCC/SRCC over regression- or ranking-based RL methods. Our findings provide a new insight into unifying regression and ranking, offering a theoretical basis for understanding quality-structure modeling in BIQA and beyond.

Response Surface Methodology (RSM) and desirability functions were employed in a case study to optimize the thermal and daylight performance of a computational model of a tropical housing typology. Specifically, this approach simultaneously optimized Indoor Overheating Hours (IOH) and Useful Daylight Illuminance (UDI) metrics through an Overall Desirability (D). The lack of significant association between IOH and other annual daylight metrics enabled a focused optimization of IOH and UDI. Each response required only 138 simulation runs (~30 hours for 276 runs) to determine the optimal values for passive strategies: window-to-wall ratio (WWR) and roof overhang depth across four orientations, totalling eight factors. First, initial screening based on 2_V^{8-2} fractional factorial design, identified four key factors using stepwise and Lasso regression, narrowed down to three: roof overhang depth on the south and west, WWR on the west, and WWR on the south. Then, RSM optimization yielded an optimal solution (roof overhang: 3.78 meters, west WWR: 3.76%, south WWR: 29.3%) with a D of 0.625 (IOH: 8.33%, UDI: 79.67%). Finally, robustness analysis with 1,000 bootstrap replications provided 95% confidence intervals for the optimal values. This study optimally balances thermal comfort and daylight with few experiments using a computationally-efficient multi-objective approach.

Hyperparameter tuning almost always means search: fit the model at every value on a grid, score each by cross-validation, and keep the winner. For spline regression that search is unnecessary. The optimal resolution can be solved for in closed form, to the accuracy an exhaustive search reaches, at a fraction of the compute. Three ingredients make this possible: classical approximation theory pins the squared bias to a known power of the resolution G, exactly the Kolmogorov n-width of the smoothness class; the basis dimension is an explicit polynomial in G; and leave-one-out error follows from a single fit via the PRESS identity. Balancing the two known curves gives the minimizer analytically. We extend this calculus to many coordinates by replacing ambient input dimension with interaction order, the number of active low-order components in an ANOVA decomposition, yielding a scaling law in which the optimal resolution and error are power functions of the effective density (sample size per active component), with input dimension absent from the exponent. The law becomes an algorithm. KORE (Kolmogorov-optimal Order-aware Resolution Estimation) fits two pilot resolutions, solves a leverage-calibrated 2x2 system for the bias and noise scales, and evaluates the closed-form plug-in resolution with a tiny leave-one-out certificate: about a dozen fits instead of a full grid sweep, with a consistency guarantee as the sample grows. Across additive and sparse pairwise targets up to 80 input dimensions, KORE matches exhaustive 3-fold cross-validation and the full classical ladder (GCV, Mallows' Cp, AIC, BIC) while fitting roughly 8x fewer models; on 36 real tabular datasets it ranks first among 21 methods in accuracy per unit of compute, ahead of tuned boosters and kernel machines. When complexity lives in low interaction order, solving for the resolution beats searching for it.

Out-of-distribution (OOD) detection holds significant importance across many applications. While semantic and domain-shift OOD problems are well-studied, this work focuses on covariate shifts - subtle variations in the data distribution that can degrade machine learning performance. We hypothesize that detecting these subtle shifts can improve our understanding of in-distribution boundaries, ultimately improving OOD detection. In adversarial discriminators trained with Batch Normalization (BN), real and adversarial samples form distinct domains with unique batch statistics - a property we exploit for OOD detection. We introduce DisCoPatch, an unsupervised Adversarial Variational Autoencoder (VAE) framework that harnesses this mechanism. During inference, batches consist of patches from the same image, ensuring a consistent data distribution that allows the model to rely on batch statistics. DisCoPatch uses the VAE's suboptimal outputs (generated and reconstructed) as negative samples to train the discriminator, thereby improving its ability to delineate the boundary between in-distribution samples and covariate shifts. By tightening this boundary, DisCoPatch achieves state-of-the-art results in public OOD detection benchmarks. The proposed model not only excels in detecting covariate shifts, achieving 95.5% AUROC on ImageNet-1K(-C) but also outperforms all prior methods on public Near-OOD (95.0%) benchmarks. With a compact model size of 25MB, it achieves high OOD detection performance at notably lower latency than existing methods, making it an efficient and practical solution for real-world OOD detection applications. The code is publicly available.

Recent hybrid video generation models combine autoregressive temporal dynamics with diffusion-based spatial denoising, but their sequential, iterative nature leads to error accumulation and long inference times. In this work, we propose a distillation-based framework for efficient causal video generation that enables high-quality synthesis with extremely limited denoising steps. Our approach builds upon the Distribution Matching Distillation (DMD) framework and proposes a novel Adversarial Self-Distillation (ASD) strategy, which aligns the outputs of the student model's n-step denoising process with its (n+1)-step version at the distribution level. This design provides smoother supervision by bridging small intra-student gaps and more informative guidance by combining teacher knowledge with locally consistent student behavior, substantially improving training stability and generation quality in extremely few-step scenarios (e.g., 1-2 steps). In addition, we present a First-Frame Enhancement (FFE) strategy, which allocates more denoising steps to the initial frames to mitigate error propagation while applying larger skipping steps to later frames. Extensive experiments on VBench demonstrate that our method surpasses state-of-the-art approaches in both one-step and two-step video generation. Notably, our framework produces a single distilled model that flexibly supports multiple inference-step settings, eliminating the need for repeated re-distillation and enabling efficient, high-quality video synthesis.

Uniform random exploration in decision-making systems supports off-policy learning via supervision but incurs high regret, making it impractical for many applications. Conversely, non-uniform exploration offers better immediate performance but lacks support for off-policy learning. Recent research suggests that regression oracles can bridge this gap by combining non-uniform exploration with supervised learning. In this paper, we analyze these approaches within a real-world industrial context at Adyen, a large global payments processor characterized by batch logged delayed feedback, short-term memory, and dynamic action spaces under the Empirical Risk Minimization (ERM) framework. Our analysis reveals that while regression oracles significantly improve performance, they introduce challenges due to rigid algorithmic assumptions. Specifically, we observe that as a policy improves, subsequent generations may perform worse due to shifts in the reward distribution and increased class imbalance in the training data. This degradation occurs de spite improvements in other aspects of the training data, leading to decreased performance in successive policy iterations. We further explore the long-term impact of regression oracles, identifying a potential "oscillation effect." This effect arises when regression oracles influence probability estimates and the realizability of subsequent policy models, leading to fluctuations in performance across iterations. Our findings highlight the need for more adaptable algorithms that can leverage the benefits of regression oracles without introducing instability in policy performance over time.

Generalizing to out-of-distribution (OOD) data or unseen domain, termed OOD generalization, still lacks appropriate theoretical guarantees. Canonical OOD bounds focus on different distance measurements between source and target domains but fail to consider the optimization property of the learned model. As empirically shown in recent work, the sharpness of learned minima influences OOD generalization. To bridge this gap between optimization and OOD generalization, we study the effect of sharpness on how a model tolerates data change in domain shift which is usually captured by "robustness" in generalization. In this paper, we give a rigorous connection between sharpness and robustness, which gives better OOD guarantees for robust algorithms. It also provides a theoretical backing for "flat minima leads to better OOD generalization". Overall, we propose a sharpness-based OOD generalization bound by taking robustness into consideration, resulting in a tighter bound than non-robust guarantees. Our findings are supported by the experiments on a ridge regression model, as well as the experiments on deep learning classification tasks.

Sparse linear regression is one of the most basic questions in machine learning and statistics. Here, we are given as input a design matrix X in R^{N times d} and measurements or labels {y} in R^N where {y} = {X} {w}^* + {xi}, and {xi} is the noise in the measurements. Importantly, we have the additional constraint that the unknown signal vector {w}^* is sparse: it has k non-zero entries where k is much smaller than the ambient dimension. Our goal is to output a prediction vector {w} that has small prediction error: 1{N}cdot |{X} {w}^* - {X} {w}|^2_2. Information-theoretically, we know what is best possible in terms of measurements: under most natural noise distributions, we can get prediction error at most epsilon with roughly N = O(k log d/epsilon) samples. Computationally, this currently needs d^{Omega(k)} run-time. Alternately, with N = O(d), we can get polynomial-time. Thus, there is an exponential gap (in the dependence on d) between the two and we do not know if it is possible to get d^{o(k)} run-time and o(d) samples. We give the first generic positive result for worst-case design matrices {X}: For any {X}, we show that if the support of {w}^* is chosen at random, we can get prediction error epsilon with N = poly(k, log d, 1/epsilon) samples and run-time poly(d,N). This run-time holds for any design matrix {X} with condition number up to 2^{poly(d)}. Previously, such results were known for worst-case {w}^*, but only for random design matrices from well-behaved families, matrices that have a very low condition number (poly(log d); e.g., as studied in compressed sensing), or those with special structural properties.

We consider the problem of estimating the optimal transport map between two probability distributions, P and Q in mathbb R^d, on the basis of i.i.d. samples. All existing statistical analyses of this problem require the assumption that the transport map is Lipschitz, a strong requirement that, in particular, excludes any examples where the transport map is discontinuous. As a first step towards developing estimation procedures for discontinuous maps, we consider the important special case where the data distribution Q is a discrete measure supported on a finite number of points in mathbb R^d. We study a computationally efficient estimator initially proposed by Pooladian and Niles-Weed (2021), based on entropic optimal transport, and show in the semi-discrete setting that it converges at the minimax-optimal rate n^{-1/2}, independent of dimension. Other standard map estimation techniques both lack finite-sample guarantees in this setting and provably suffer from the curse of dimensionality. We confirm these results in numerical experiments, and provide experiments for other settings, not covered by our theory, which indicate that the entropic estimator is a promising methodology for other discontinuous transport map estimation problems.

We consider in this paper the problem of optimal experiment design where a decision maker can choose which points to sample to obtain an estimate hatβ of the hidden parameter β^{star} of an underlying linear model. The key challenge of this work lies in the heteroscedasticity assumption that we make, meaning that each covariate has a different and unknown variance. The goal of the decision maker is then to figure out on the fly the optimal way to allocate the total budget of T samples between covariates, as sampling several times a specific one will reduce the variance of the estimated model around it (but at the cost of a possible higher variance elsewhere). By trying to minimize the ell^2-loss E [lVerthatβ-β^{star}rVert^2] the decision maker is actually minimizing the trace of the covariance matrix of the problem, which corresponds then to online A-optimal design. Combining techniques from bandit and convex optimization we propose a new active sampling algorithm and we compare it with existing ones. We provide theoretical guarantees of this algorithm in different settings, including a O(T^{-2}) regret bound in the case where the covariates form a basis of the feature space, generalizing and improving existing results. Numerical experiments validate our theoretical findings.

An essential and challenging problem in causal inference is causal effect estimation from observational data. The problem becomes more difficult with the presence of unobserved confounding variables. The front-door adjustment is a practical approach for dealing with unobserved confounding variables. However, the restriction for the standard front-door adjustment is difficult to satisfy in practice. In this paper, we relax some of the restrictions by proposing the concept of conditional front-door (CFD) adjustment and develop the theorem that guarantees the causal effect identifiability of CFD adjustment. Furthermore, as it is often impossible for a CFD variable to be given in practice, it is desirable to learn it from data. By leveraging the ability of deep generative models, we propose CFDiVAE to learn the representation of the CFD adjustment variable directly from data with the identifiable Variational AutoEncoder and formally prove the model identifiability. Extensive experiments on synthetic datasets validate the effectiveness of CFDiVAE and its superiority over existing methods. The experiments also show that the performance of CFDiVAE is less sensitive to the causal strength of unobserved confounding variables. We further apply CFDiVAE to a real-world dataset to demonstrate its potential application.

Should prediction models always deliver a prediction? In the pursuit of maximum predictive performance, critical considerations of reliability and fairness are often overshadowed, particularly when it comes to the role of uncertainty. Selective regression, also known as the "reject option," allows models to abstain from predictions in cases of considerable uncertainty. Initially proposed seven decades ago, approaches to selective regression have mostly focused on distribution-based proxies for measuring uncertainty, particularly conditional variance. However, this focus neglects the significant influence of model-specific biases on a model's performance. In this paper, we propose a novel approach to selective regression by leveraging conformal prediction, which provides grounded confidence measures for individual predictions based on model-specific biases. In addition, we propose a standardized evaluation framework to allow proper comparison of selective regression approaches. Via an extensive experimental approach, we demonstrate how our proposed approach, conformalized selective regression, demonstrates an advantage over multiple state-of-the-art baselines.

The extant insurance literature demonstrates a paucity of finite-sample valid prediction intervals of future insurance claims in the regression setting. To address this challenge, this article proposes a new strategy that converts a predictive method in the unsupervised iid (independent identically distributed) setting to a predictive method in the regression setting. In particular, it enables an actuary to obtain infinitely many finite-sample valid prediction intervals in the regression setting.

We study the problem of single-image zero-shot 3D shape reconstruction. Recent works learn zero-shot shape reconstruction through generative modeling of 3D assets, but these models are computationally expensive at train and inference time. In contrast, the traditional approach to this problem is regression-based, where deterministic models are trained to directly regress the object shape. Such regression methods possess much higher computational efficiency than generative methods. This raises a natural question: is generative modeling necessary for high performance, or conversely, are regression-based approaches still competitive? To answer this, we design a strong regression-based model, called ZeroShape, based on the converging findings in this field and a novel insight. We also curate a large real-world evaluation benchmark, with objects from three different real-world 3D datasets. This evaluation benchmark is more diverse and an order of magnitude larger than what prior works use to quantitatively evaluate their models, aiming at reducing the evaluation variance in our field. We show that ZeroShape not only achieves superior performance over state-of-the-art methods, but also demonstrates significantly higher computational and data efficiency.

Gradients can be employed for sensitivity analysis. Here, we leverage the advantages of the Loss Landscape to comprehend which independent variables impact the dependent variable. We seek to grasp the loss landscape by utilizing first, second, and third derivatives through automatic differentiation. we know that Spearman's rank correlation coefficient can detect the monotonic relationship between two variables. However, I have found that second-order gradients, with certain configurations and parameters, provide information that can be visualized similarly to Spearman results, In this approach, we incorporate a loss function with an activation function, resulting in a non-linear pattern. Each exploration of the loss landscape through retraining yields new valuable information. Furthermore, the first and third derivatives are also beneficial, as they indicate the extent to which independent variables influence the dependent variable.

Converting a pretrained Transformer into a more efficient hybrid model through distillation offers a promising approach to reducing inference costs. However, achieving high-quality generation in distilled models requires careful joint design of both the student architecture and the distillation process. Many prior distillation works evaluate downstream multiple-choice benchmarks by ranking candidate answers with log-likelihood rather than requiring autoregressive generation, which can obscure important differences in model quality. For example, we show that a 7B parameter distilled model that nearly matches its teacher to within 0.2\,pp under log-likelihood scoring actually falls behind by 20.8\,pp when the model must generate answers autoregressively. We propose a Hybrid Kimi Delta Attention (Hybrid-KDA) architecture paired with GenDistill, a multi-stage distillation pipeline, and use generation-based evaluation throughout to guide design decisions. Applying this approach to Qwen3-0.6B, we systematically ablate six design axes: training objective, loss masking, training duration, dataset selection, parameter freezing, and architecture choice. We find that log-likelihood-based evaluation consistently underestimates the gap between teacher and student, and can in some cases reverse the ranking of design choices, meaning that conclusions drawn from perplexity-only evaluation may be misleading. Among the factors we study, dataset selection, completion-only masking, and freezing attention layers during post-training have the largest impact on generation quality. Our best Hybrid-KDA model retains 86--90\% of teacher accuracy on knowledge benchmarks while reducing KV cache memory by up to 75\% and improving time-to-first-token by 2--4times at 128K-token contexts.

OptiWing3D is the first publicly available dataset of high-fidelity shape optimized 3D wing geometries. Existing aerodynamics datasets are either limited to 2D simulations, lack optimization, or derive diversity solely from perturbations to a single baseline design, constraining their application as benchmarks to inverse design approaches and in the study of design diversity. The OptiWing3D dataset addresses these gaps, consisting of 1552 simulations resulting in 776 wing designs initialized from distinct extruded airfoil cross-sections. Additionally, a majority of the optimized wings in the dataset are paired to 2D counterparts optimized under identical conditions, creating the first multi-fidelity aerodynamic shape optimization dataset. Moreover, this structure allows for a direct comparison between 2D and 3D aerodynamic simulations. It is observed that 3D optimized designs diverge most prominently from the 2D-optimized designs near the wingtip, where three-dimensional effects are strongest, a finding made possible by the paired nature of the dataset. Finally, we demonstrate a constraint-aware conditional latent diffusion model capable of generating optimized wings from flow conditions, establishing a baseline for future inverse design approaches. The dataset, containing wing geometries and surface pressure distributions is publicly released to advance research in data-driven aerodynamic design.

Calibration measures and reliability diagrams are two fundamental tools for measuring and interpreting the calibration of probabilistic predictors. Calibration measures quantify the degree of miscalibration, and reliability diagrams visualize the structure of this miscalibration. However, the most common constructions of reliability diagrams and calibration measures -- binning and ECE -- both suffer from well-known flaws (e.g. discontinuity). We show that a simple modification fixes both constructions: first smooth the observations using an RBF kernel, then compute the Expected Calibration Error (ECE) of this smoothed function. We prove that with a careful choice of bandwidth, this method yields a calibration measure that is well-behaved in the sense of (B{\l}asiok, Gopalan, Hu, and Nakkiran 2023a) -- a consistent calibration measure. We call this measure the SmoothECE. Moreover, the reliability diagram obtained from this smoothed function visually encodes the SmoothECE, just as binned reliability diagrams encode the BinnedECE. We also provide a Python package with simple, hyperparameter-free methods for measuring and plotting calibration: `pip install relplot\`.

We propose a penalized nonparametric approach to estimating the quantile regression process (QRP) in a nonseparable model using rectifier quadratic unit (ReQU) activated deep neural networks and introduce a novel penalty function to enforce non-crossing of quantile regression curves. We establish the non-asymptotic excess risk bounds for the estimated QRP and derive the mean integrated squared error for the estimated QRP under mild smoothness and regularity conditions. To establish these non-asymptotic risk and estimation error bounds, we also develop a new error bound for approximating C^s smooth functions with s >0 and their derivatives using ReQU activated neural networks. This is a new approximation result for ReQU networks and is of independent interest and may be useful in other problems. Our numerical experiments demonstrate that the proposed method is competitive with or outperforms two existing methods, including methods using reproducing kernels and random forests, for nonparametric quantile regression.

Symbolic regression (SR) aims to discover closed-form mathematical expressions that accurately describe data, offering interpretability and analytical insight beyond standard black-box models. Existing SR methods often rely on population-based search or autoregressive modeling, which struggle with scalability and symbolic consistency. We introduce LIES (Logarithm, Identity, Exponential, Sine), a fixed neural network architecture with interpretable primitive activations that are optimized to model symbolic expressions. We develop a framework to extract compact formulae from LIES networks by training with an appropriate oversampling strategy and a tailored loss function to promote sparsity and to prevent gradient instability. After training, it applies additional pruning strategies to further simplify the learned expressions into compact formulae. Our experiments on SR benchmarks show that the LIES framework consistently produces sparse and accurate symbolic formulae outperforming all baselines. We also demonstrate the importance of each design component through ablation studies.

This paper proposes a method for the automatic creation of variables (in the case of regression) that complement the information contained in the initial input vector. The method works as a pre-processing step in which the continuous values of the variable to be regressed are discretized into a set of intervals which are then used to define value thresholds. Then classifiers are trained to predict whether the value to be regressed is less than or equal to each of these thresholds. The different outputs of the classifiers are then concatenated in the form of an additional vector of variables that enriches the initial vector of the regression problem. The implemented system can thus be considered as a generic pre-processing tool. We tested the proposed enrichment method with 5 types of regressors and evaluated it in 33 regression datasets. Our experimental results confirm the interest of the approach.

Bayesian optimal experimental design is a sub-field of statistics focused on developing methods to make efficient use of experimental resources. Any potential design is evaluated in terms of a utility function, such as the (theoretically well-justified) expected information gain (EIG); unfortunately however, under most circumstances the EIG is intractable to evaluate. In this work we build off of successful variational approaches, which optimize a parameterized variational model with respect to bounds on the EIG. Past work focused on learning a new variational model from scratch for each new design considered. Here we present a novel neural architecture that allows experimenters to optimize a single variational model that can estimate the EIG for potentially infinitely many designs. To further improve computational efficiency, we also propose to train the variational model on a significantly cheaper-to-evaluate lower bound, and show empirically that the resulting model provides an excellent guide for more accurate, but expensive to evaluate bounds on the EIG. We demonstrate the effectiveness of our technique on generalized linear models, a class of statistical models that is widely used in the analysis of controlled experiments. Experiments show that our method is able to greatly improve accuracy over existing approximation strategies, and achieve these results with far better sample efficiency.

Previous works on Treatment Effect Estimation (TEE) are not in widespread use because they are predominantly theoretical, where strong parametric assumptions are made but untractable for practical application. Recent work uses multilayer perceptron (MLP) for modeling casual relationships, however, MLPs lag far behind recent advances in ML methodology, which limits their applicability and generalizability. To extend beyond the single domain formulation and towards more realistic learning scenarios, we explore model design spaces beyond MLPs, i.e., transformer backbones, which provide flexibility where attention layers govern interactions among treatments and covariates to exploit structural similarities of potential outcomes for confounding control. Through careful model design, Transformers as Treatment Effect Estimators (TransTEE) is proposed. We show empirically that TransTEE can: (1) serve as a general purpose treatment effect estimator that significantly outperforms competitive baselines in a variety of challenging TEE problems (e.g., discrete, continuous, structured, or dosage-associated treatments) and is applicable to both when covariates are tabular and when they consist of structural data (e.g., texts, graphs); (2) yield multiple advantages: compatibility with propensity score modeling, parameter efficiency, robustness to continuous treatment value distribution shifts, explainable in covariate adjustment, and real-world utility in auditing pre-trained language models

Completely randomized experiments, originally developed by Fisher and Neyman in the 1930s, are still widely used in practice, even in online experimentation. However, such designs are of limited value for answering standard questions in marketplaces, where multiple populations of agents interact strategically, leading to complex patterns of spillover effects. In this paper, we derive the finite-sample properties of tractable estimators for "Simple Multiple Randomization Designs" (SMRDs), a new class of experimental designs which account for complex spillover effects in randomized experiments. Our derivations are obtained under a natural and general form of cross-unit interference, which we call "local interference". We discuss the estimation of main effects, direct effects, and spillovers, and present associated central limit theorems.

Out-of-distribution (OOD) prediction is often approached by restricting models to causal or invariant covariates, avoiding non-causal spurious associations that may be unstable across environments. Despite its theoretical appeal, this strategy frequently underperforms empirical risk minimization (ERM) in practice. We investigate the source of this gap and show that such failures naturally arise when only a subset of the true causes of the outcome is observed. In these settings, non-causal spurious covariates can serve as informative proxies for unobserved causes and substantially improve prediction, except under distribution shifts that break these proxy relationships. Consequently, the optimal set of predictive covariates is neither universal nor necessarily exhibits invariant relationships with the outcome across all environments, but instead depends on the specific type of shift encountered. Crucially, we observe that different covariate shifts induce distinct, observable signatures in the covariate distribution itself. Moreover, these signatures can be extracted from unlabeled data in the target OOD environment and used to assess when proxy covariates remain reliable and when they fail. Building on this observation, we propose an environment-adaptive covariate selection (EACS) algorithm that maps environment-level covariate summaries to environment-specific covariate sets, while allowing the incorporation of prior causal knowledge as constraints. Across simulations and applied datasets, EACS consistently outperforms static causal, invariant, and ERM-based predictors under diverse distribution shifts.

The relationship between material properties and independent variables such as temperature, external field or time, is usually represented by a curve or surface in a multi-dimensional space. Determining such a curve or surface requires a series of experiments or calculations which are often time and cost consuming. A general strategy uses an appropriate utility function to sample the space to recommend the next optimal experiment or calculation within an active learning loop. However, knowing what the optimal sampling strategy to use to minimize the number of experiments is an outstanding problem. We compare a number of strategies based on directed exploration on several materials problems of varying complexity using a Kriging based model. These include one dimensional curves such as the fatigue life curve for 304L stainless steel and the Liquidus line of the Fe-C phase diagram, surfaces such as the Hartmann 3 function in 3D space and the fitted intermolecular potential for Ar-SH, and a four dimensional data set of experimental measurements for BaTiO3 based ceramics. We also consider the effects of experimental noise on the Hartmann 3 function. We find that directed exploration guided by maximum variance provides better performance overall, converging faster across several data sets. However, for certain problems, the trade-off methods incorporating exploitation can perform at least as well, if not better than maximum variance. Thus, we discuss how the choice of the utility function depends on the distribution of the data, the model performance and uncertainties, additive noise as well as the budget.

In observational settings where treatment and outcome share unmeasured confounders but an observed mediator remains unconfounded, the front-door (FD) adjustment identifies causal effects through the mediator. We study the heterogeneous treatment effect (HTE) under FD identification and introduce two debiased learners: FD-DR-Learner and FD-R-Learner. Both attain fast, quasi-oracle rates (i.e., performance comparable to an oracle that knows the nuisances) even when nuisance functions converge as slowly as n^-1/4. We provide error analyses establishing debiasedness and demonstrate robust empirical performance in synthetic studies and a real-world case study of primary seat-belt laws using Fatality Analysis Reporting System (FARS) dataset. Together, these results indicate that the proposed learners deliver reliable and sample-efficient HTE estimates in FD scenarios. The implementation is available at https://github.com/yonghanjung/FD-CATE. Keywords: Front-door adjustment; Heterogeneous treatment effects; Debiased learning; Quasi-oracle rates; Causal inference.

Foundation models are often used as fixed black-box predictors for downstream tasks with limited labeled data, but their predictions may be biased and unsafe to trust blindly. We study this setting through black-box assisted nonparametric regression: a learner observes labeled samples and can query a fixed predictor f_0, while the target f^* is close to f_0 in L_2(P_X) up to an unknown radius δ. We give a finite-sample minimax characterization showing a phase transition at δ_c(n) asymp n^{-β/(2β+d)}, with leading risk min{δ^2, n^{-2β/(2β+d)}}. We then analyze a Safe Residual Estimator: it learns a correction around f_0, initializes the residual head at zero so the initial predictor equals f_0, and uses holdout selection to revert to f_0 when the learned correction is not supported by validation data. Here, "safe" means avoiding negative transfer, i.e., performing worse than the black-box predictor alone. The estimator matches the leading minimax term up to an additive validation-selection cost. Synthetic regression experiments verify the predicted phase transition, while CIFAR-100 with CLIP and AG News with Qwen3-8B provide practice-facing evidence that the same residual-correction tradeoff is useful beyond the formal squared-loss regression setting.

A directed acyclic graph (DAG) provides valuable prior knowledge that is often discarded in regression tasks in machine learning. We show that the independences arising from the presence of collider structures in DAGs provide meaningful inductive biases, which constrain the regression hypothesis space and improve predictive performance. We introduce collider regression, a framework to incorporate probabilistic causal knowledge from a collider in a regression problem. When the hypothesis space is a reproducing kernel Hilbert space, we prove a strictly positive generalisation benefit under mild assumptions and provide closed-form estimators of the empirical risk minimiser. Experiments on synthetic and climate model data demonstrate performance gains of the proposed methodology.

In this review, we present econometric and statistical methods for analyzing randomized experiments. For basic experiments we stress randomization-based inference as opposed to sampling-based inference. In randomization-based inference, uncertainty in estimates arises naturally from the random assignment of the treatments, rather than from hypothesized sampling from a large population. We show how this perspective relates to regression analyses for randomized experiments. We discuss the analyses of stratified, paired, and clustered randomized experiments, and we stress the general efficiency gains from stratification. We also discuss complications in randomized experiments such as non-compliance. In the presence of non-compliance we contrast intention-to-treat analyses with instrumental variables analyses allowing for general treatment effect heterogeneity. We consider in detail estimation and inference for heterogeneous treatment effects in settings with (possibly many) covariates. These methods allow researchers to explore heterogeneity by identifying subpopulations with different treatment effects while maintaining the ability to construct valid confidence intervals. We also discuss optimal assignment to treatment based on covariates in such settings. Finally, we discuss estimation and inference in experiments in settings with interactions between units, both in general network settings and in settings where the population is partitioned into groups with all interactions contained within these groups.

Tuning the regularization parameter in penalized regression models is an expensive task, requiring multiple models to be fit along a path of parameters. Strong screening rules drastically reduce computational costs by lowering the dimensionality of the input prior to fitting. We develop strong screening rules for group-based Sorted L-One Penalized Estimation (SLOPE) models: Group SLOPE and Sparse-group SLOPE. The developed rules are applicable to the wider family of group-based OWL models, including OSCAR. Our experiments on both synthetic and real data show that the screening rules significantly accelerate the fitting process. The screening rules make it accessible for group SLOPE and sparse-group SLOPE to be applied to high-dimensional datasets, particularly those encountered in genetics.

We consider the classic supervised learning problem, where a continuous non-negative random label Y (i.e. a random duration) is to be predicted based upon observing a random vector X valued in R^d with dgeq 1 by means of a regression rule with minimum least square error. In various applications, ranging from industrial quality control to public health through credit risk analysis for instance, training observations can be right censored, meaning that, rather than on independent copies of (X,Y), statistical learning relies on a collection of ngeq 1 independent realizations of the triplet (X, ; min{Y,; C},; δ), where C is a nonnegative r.v. with unknown distribution, modeling censorship and δ=I{Yleq C} indicates whether the duration is right censored or not. As ignoring censorship in the risk computation may clearly lead to a severe underestimation of the target duration and jeopardize prediction, we propose to consider a plug-in estimate of the true risk based on a Kaplan-Meier estimator of the conditional survival function of the censorship C given X, referred to as Kaplan-Meier risk, in order to perform empirical risk minimization. It is established, under mild conditions, that the learning rate of minimizers of this biased/weighted empirical risk functional is of order O_{P}(log(n)/n) when ignoring model bias issues inherent to plug-in estimation, as can be attained in absence of censorship. Beyond theoretical results, numerical experiments are presented in order to illustrate the relevance of the approach developed.

The quality of many modern machine learning models improves as model complexity increases, an effect that has been quantified, for predictive performance, with the non-monotonic double descent learning curve. Here, we address the overarching question: is there an analogous theory of double descent for models which estimate uncertainty? We provide a partially affirmative and partially negative answer in the setting of Gaussian processes (GP). Under standard assumptions, we prove that higher model quality for optimally-tuned GPs (including uncertainty prediction) under marginal likelihood is realized for larger input dimensions, and therefore exhibits a monotone error curve. After showing that marginal likelihood does not naturally exhibit double descent in the input dimension, we highlight related forms of posterior predictive loss that do exhibit non-monotonicity. Finally, we verify empirically that our results hold for real data, beyond our considered assumptions, and we explore consequences involving synthetic covariates.

Regression, the task of predicting a continuous scalar target y based on some features x is one of the most fundamental tasks in machine learning and statistics. It has been observed and theoretically analyzed that the classical approach, meansquared error minimization, can lead to suboptimal results when training neural networks. In this work, we propose a new method to improve the training of these models on regression tasks, with continuous scalar targets. Our method is based on casting this task in a different fashion, using a target encoder, and a prediction decoder, inspired by approaches in classification and clustering. We showcase the performance of our method on a wide range of real-world datasets.

We introduce a gradient-based approach for the problem of Bayesian optimal experimental design to learn causal models in a batch setting -- a critical component for causal discovery from finite data where interventions can be costly or risky. Existing methods rely on greedy approximations to construct a batch of experiments while using black-box methods to optimize over a single target-state pair to intervene with. In this work, we completely dispose of the black-box optimization techniques and greedy heuristics and instead propose a conceptually simple end-to-end gradient-based optimization procedure to acquire a set of optimal intervention target-state pairs. Such a procedure enables parameterization of the design space to efficiently optimize over a batch of multi-target-state interventions, a setting which has hitherto not been explored due to its complexity. We demonstrate that our proposed method outperforms baselines and existing acquisition strategies in both single-target and multi-target settings across a number of synthetic datasets.

Diffusion models (DMs) have revolutionized generative learning. They utilize a diffusion process to encode data into a simple Gaussian distribution. However, encoding a complex, potentially multimodal data distribution into a single continuous Gaussian distribution arguably represents an unnecessarily challenging learning problem. We propose Discrete-Continuous Latent Variable Diffusion Models (DisCo-Diff) to simplify this task by introducing complementary discrete latent variables. We augment DMs with learnable discrete latents, inferred with an encoder, and train DM and encoder end-to-end. DisCo-Diff does not rely on pre-trained networks, making the framework universally applicable. The discrete latents significantly simplify learning the DM's complex noise-to-data mapping by reducing the curvature of the DM's generative ODE. An additional autoregressive transformer models the distribution of the discrete latents, a simple step because DisCo-Diff requires only few discrete variables with small codebooks. We validate DisCo-Diff on toy data, several image synthesis tasks as well as molecular docking, and find that introducing discrete latents consistently improves model performance. For example, DisCo-Diff achieves state-of-the-art FID scores on class-conditioned ImageNet-64/128 datasets with ODE sampler.

Breakthroughs in machine learning are rapidly changing science and society, yet our fundamental understanding of this technology has lagged far behind. Indeed, one of the central tenets of the field, the bias-variance trade-off, appears to be at odds with the observed behavior of methods used in the modern machine learning practice. The bias-variance trade-off implies that a model should balance under-fitting and over-fitting: rich enough to express underlying structure in data, simple enough to avoid fitting spurious patterns. However, in the modern practice, very rich models such as neural networks are trained to exactly fit (i.e., interpolate) the data. Classically, such models would be considered over-fit, and yet they often obtain high accuracy on test data. This apparent contradiction has raised questions about the mathematical foundations of machine learning and their relevance to practitioners. In this paper, we reconcile the classical understanding and the modern practice within a unified performance curve. This "double descent" curve subsumes the textbook U-shaped bias-variance trade-off curve by showing how increasing model capacity beyond the point of interpolation results in improved performance. We provide evidence for the existence and ubiquity of double descent for a wide spectrum of models and datasets, and we posit a mechanism for its emergence. This connection between the performance and the structure of machine learning models delineates the limits of classical analyses, and has implications for both the theory and practice of machine learning.

Data-driven modeling in real-world regression tasks often suffers from limited training samples, high collection costs, and noisy observations. Inspired by the impact of data augmentation in vision and language, we propose a novel Counterfactual Residual Data Augmentation (CRDA) technique for tabular regression. Our key insight is that once a regressor has modeled the systematic component of the data, the remaining noise can be viewed as an invariant residual that remains stable under small perturbations of carefully selected features. We exploit this residual invariance to generate new, yet realistic, training samples, effectively expanding the dataset without requiring additional real data. Our method is model-agnostic and readily applicable to various types of regressors. In experiments across datasets from a variety of benchmark repositories, on average, CRDA reduces an MLP Regressor's MSE by 22.9% and an XGBoost Regressor's MSE by 6.4%. When compared to existing state-of-the-art data generators and augmentation techniques, CRDA consistently outperforms in MSE reduction. By adding principled counterfactual variations to the training data, our method offers a simple and efficient remedy for noise-prone, small-sample regression settings.

Offline reinforcement learning enables agents to leverage large pre-collected datasets of environment transitions to learn control policies, circumventing the need for potentially expensive or unsafe online data collection. Significant progress has been made recently in offline model-based reinforcement learning, approaches which leverage a learned dynamics model. This typically involves constructing a probabilistic model, and using the model uncertainty to penalize rewards where there is insufficient data, solving for a pessimistic MDP that lower bounds the true MDP. Existing methods, however, exhibit a breakdown between theory and practice, whereby pessimistic return ought to be bounded by the total variation distance of the model from the true dynamics, but is instead implemented through a penalty based on estimated model uncertainty. This has spawned a variety of uncertainty heuristics, with little to no comparison between differing approaches. In this paper, we compare these heuristics, and design novel protocols to investigate their interaction with other hyperparameters, such as the number of models, or imaginary rollout horizon. Using these insights, we show that selecting these key hyperparameters using Bayesian Optimization produces superior configurations that are vastly different to those currently used in existing hand-tuned state-of-the-art methods, and result in drastically stronger performance.

Deep regression models typically learn in an end-to-end fashion without explicitly emphasizing a regression-aware representation. Consequently, the learned representations exhibit fragmentation and fail to capture the continuous nature of sample orders, inducing suboptimal results across a wide range of regression tasks. To fill the gap, we propose Rank-N-Contrast (RNC), a framework that learns continuous representations for regression by contrasting samples against each other based on their rankings in the target space. We demonstrate, theoretically and empirically, that RNC guarantees the desired order of learned representations in accordance with the target orders, enjoying not only better performance but also significantly improved robustness, efficiency, and generalization. Extensive experiments using five real-world regression datasets that span computer vision, human-computer interaction, and healthcare verify that RNC achieves state-of-the-art performance, highlighting its intriguing properties including better data efficiency, robustness to spurious targets and data corruptions, and generalization to distribution shifts. Code is available at: https://github.com/kaiwenzha/Rank-N-Contrast.

We present ConDiff, a novel dataset for scientific machine learning. ConDiff focuses on the parametric diffusion equation with space dependent coefficients, a fundamental problem in many applications of partial differential equations (PDEs). The main novelty of the proposed dataset is that we consider discontinuous coefficients with high contrast. These coefficient functions are sampled from a selected set of distributions. This class of problems is not only of great academic interest, but is also the basis for describing various environmental and industrial problems. In this way, ConDiff shortens the gap with real-world problems while remaining fully synthetic and easy to use. ConDiff consists of a diverse set of diffusion equations with coefficients covering a wide range of contrast levels and heterogeneity with a measurable complexity metric for clearer comparison between different coefficient functions. We baseline ConDiff on standard deep learning models in the field of scientific machine learning. By providing a large number of problem instances, each with its own coefficient function and right-hand side, we hope to encourage the development of novel physics-based deep learning approaches, such as neural operators, ultimately driving progress towards more accurate and efficient solutions of complex PDE problems.

Flight diversions are rare but high-impact events in aviation, making their reliable prediction vital for both safety and operational efficiency. However, their scarcity in historical records impedes the training of machine learning models utilised to predict them. This study addresses this scarcity gap by investigating how generative models can augment historical flight data with synthetic diversion records to enhance model training and improve predictive accuracy. We propose a multi-objective optimisation framework coupled with automated hyperparameter search to identify optimal configurations for three deep generative models: Tabular Variational Autoencoder (TVAE), Conditional Tabular Generative Adversarial Network (CTGAN), and CopulaGAN, with the Gaussian Copula (GC) model serving as a statistical baseline. The quality of the synthetic data was examined through a six-stage evaluation framework encompassing realism, diversity, operational validity, statistical similarity, fidelity, and predictive utility. Results show that the optimised models significantly outperform their non-optimised counterparts, and that synthetic augmentation substantially improves diversion prediction compared to models trained solely on real data. These findings demonstrate the effectiveness of hyperparameter-optimised generative models for advancing predictive modelling of rare events in air transportation.

Estimating the causal effects of interventions is crucial to policy and decision-making, yet outcome data are often missing or subject to non-standard measurement error. While ground-truth outcomes can sometimes be obtained through costly data annotation or follow-up, budget constraints typically allow only a fraction of the dataset to be labeled. We address this challenge by optimizing which data points should be sampled for outcome information in order to improve efficiency in average treatment effect estimation with missing outcomes. We derive a closed-form solution for the optimal batch sampling probability by minimizing the asymptotic variance of a doubly robust estimator for causal inference with missing outcomes. Motivated by our street outreach partners, we extend the framework to costly annotations of unstructured data, such as text or images in healthcare and social services. Across simulated and real-world datasets, including one of outreach interventions in homelessness services, our approach achieves substantially lower mean-squared error and recovers the AIPW estimate with fewer labels than existing baselines. In practice, we show that our method can match confidence intervals obtained with 361 random samples using only 90 optimized samples - saving 75% of the labeling budget.

This paper presents a computationally feasible method to compute rigorous bounds on the interval-generalisation of regression analysis to account for epistemic uncertainty in the output variables. The new iterative method uses machine learning algorithms to fit an imprecise regression model to data that consist of intervals rather than point values. The method is based on a single-layer interval neural network which can be trained to produce an interval prediction. It seeks parameters for the optimal model that minimizes the mean squared error between the actual and predicted interval values of the dependent variable using a first-order gradient-based optimization and interval analysis computations to model the measurement imprecision of the data. An additional extension to a multi-layer neural network is also presented. We consider the explanatory variables to be precise point values, but the measured dependent values are characterized by interval bounds without any probabilistic information. The proposed iterative method estimates the lower and upper bounds of the expectation region, which is an envelope of all possible precise regression lines obtained by ordinary regression analysis based on any configuration of real-valued points from the respective y-intervals and their x-values.

Vibe design agents turn natural-language briefs into rendered interfaces and frontend code. Yet a useful design agent should do more than produce one valid page: it should help users explore coherent alternatives. Increasing token-level temperature is a blunt solution because it varies aesthetic decisions and syntax-sensitive code at the same time. We instead separate exploration from implementation through an inference architecture that makes design direction an explicit intermediate decision. Inspired by Verbalized Sampling, a pre-pass proposes structured design specifications with typicality scores, an external selector samples one, and the downstream generator realizes the selected specification together with the original request under fixed settings. We apply this approach to UI themes and visual-asset prompts. Across 168 prompts, with 1,255 paired comparisons per temperature for each intervention, theme sampling broadens observed selection coverage and screenshot variation, while LLM-judge preferences vary across interventions, prompt complexity, and viewport. In an online experiment with more than 300,000 tasks, the observed code-export increase remains statistically uncertain, while fewer negative feedback events coexist with more correction interactions and modest operational costs. Together, these findings identify structured design specifications as a practical control point for exploring alternative UI concepts while keeping downstream generation settings fixed.

This paper addresses a regression problem in which output label values are the results of sensing the magnitude of a phenomenon. A low value of such labels can mean either that the actual magnitude of the phenomenon was low or that the sensor made an incomplete observation. This leads to a bias toward lower values in labels and the resultant learning because labels may have lower values due to incomplete observations, even if the actual magnitude of the phenomenon was high. Moreover, because an incomplete observation does not provide any tags indicating incompleteness, we cannot eliminate or impute them. To address this issue, we propose a learning algorithm that explicitly models incomplete observations corrupted with an asymmetric noise that always has a negative value. We show that our algorithm is unbiased as if it were learned from uncorrupted data that does not involve incomplete observations. We demonstrate the advantages of our algorithm through numerical experiments.

In personalized marketing, uplift models estimate incremental effects by modeling how customer behavior changes under alternative treatments. However, real-world data often exhibit biases - such as selection bias, spillover effects, and unobserved confounding - which adversely affect both estimation accuracy and metric validity. Despite the importance of bias-aware assessment, a lack of systematic studies persists. To bridge this gap, we design a systematic benchmarking framework. Unlike standard predictive tasks, real-world uplift datasets lack counterfactual ground truth, rendering direct metric validation infeasible. Therefore, a semi-synthetic approach serves as a critical enabler for systematic benchmarking, effectively bridging the gap by retaining real-world feature dependencies while providing the ground truth needed to isolate structural biases. Our investigations reveal that: (i) uplift targeting and prediction can manifest as distinct objectives, where proficiency in one does not ensure efficacy in the other; (ii) while many models exhibit inconsistent performance under diverse biases, TARNet shows notable robustness, providing insights for subsequent model design; (iii) evaluation metric stability is linked to mathematical alignment with the ATE, suggesting that ATE-approximating metrics yield more consistent model rankings under structural data imperfections. These findings suggest the need for more robust uplift models and metrics. Code will be released upon acceptance.

Understanding causality should be a core requirement of any attempt to build real impact through AI. Due to the inherent unobservability of counterfactuals, large randomised trials (RCTs) are the standard for causal inference. But large experiments are generically expensive, and randomisation carries its own costs, e.g. when suboptimal decisions are trialed. Recent work has proposed more sample-efficient alternatives to RCTs, but these are not adaptable to the downstream application for which the causal effect is sought. In this work, we develop a task-specific approach to experimental design and derive sampling strategies customised to particular downstream applications. Across a range of important tasks, real-world datasets, and sample sizes, our method outperforms other benchmarks, e.g. requiring an order-of-magnitude less data to match RCT performance on targeted marketing tasks.

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization trick is applicable when we can simulate a random variable by applying a differentiable deterministic function on an auxiliary random variable whose distribution is fixed. For many distributions of interest (such as the gamma or Dirichlet), simulation of random variables relies on acceptance-rejection sampling. The discontinuity introduced by the accept-reject step means that standard reparameterization tricks are not applicable. We propose a new method that lets us leverage reparameterization gradients even when variables are outputs of a acceptance-rejection sampling algorithm. Our approach enables reparameterization on a larger class of variational distributions. In several studies of real and synthetic data, we show that the variance of the estimator of the gradient is significantly lower than other state-of-the-art methods. This leads to faster convergence of stochastic gradient variational inference.

We develop a data-driven information-theoretic framework for sharp partial identification of causal effects under unmeasured confounding. Existing approaches often rely on restrictive assumptions, such as bounded or discrete outcomes; require external inputs (for example, instrumental variables, proxies, or user-specified sensitivity parameters); necessitate full structural causal model specifications; or focus solely on population-level averages while neglecting covariate-conditional effects. We overcome all four limitations simultaneously by establishing novel information-theoretic, data-driven divergence bounds. Our key theoretical contribution shows that the f-divergence between the observational distribution P(Y | A = a, X = x) and the interventional distribution P(Y | do(A = a), X = x) is upper bounded by a function of the propensity score alone. This result enables sharp partial identification of conditional causal effects directly from observational data, without requiring external sensitivity parameters, auxiliary variables, full structural specifications, or outcome boundedness assumptions. For practical implementation, we develop a semiparametric estimator satisfying Neyman orthogonality (Chernozhukov et al., 2018), which ensures root-n consistent inference even when nuisance functions are estimated via flexible machine learning methods. Simulation studies and real-world data applications, implemented in the GitHub repository (https://github.com/yonghanjung/Information-Theretic-Bounds), demonstrate that our framework provides tight and valid causal bounds across a wide range of data-generating processes.

Recent research shows that when Gradient Descent (GD) is applied to neural networks, the loss almost never decreases monotonically. Instead, the loss oscillates as gradient descent converges to its ''Edge of Stability'' (EoS). Here, we find a quantity that does decrease monotonically throughout GD training: the sharpness attained by the gradient flow solution (GFS)-the solution that would be obtained if, from now until convergence, we train with an infinitesimal step size. Theoretically, we analyze scalar neural networks with the squared loss, perhaps the simplest setting where the EoS phenomena still occur. In this model, we prove that the GFS sharpness decreases monotonically. Using this result, we characterize settings where GD provably converges to the EoS in scalar networks. Empirically, we show that GD monotonically decreases the GFS sharpness in a squared regression model as well as practical neural network architectures.

Many benchmarks for automated causal inference evaluate a system's performance based on a single numerical output, such as an Average Treatment Effect (ATE). This approach conflates two distinct steps in causal analysis: identification-formulating a valid research design under stated assumptions-and estimation-implementing that design numerically on finite data. We introduce CausalReasoningBenchmark, a benchmark of 173 queries across 138 real-world datasets, curated from 85 peer-reviewed research papers and four widely-used causal-inference textbooks. For each query a system must produce (i) a structured identification specification that names the strategy, the treatment, outcome, and control variables, and all design-specific elements, and (ii) a point estimate with a standard error. By scoring these two components separately, our benchmark enables granular diagnosis: it distinguishes failures in causal reasoning from errors in numerical execution. Baseline results with a state-of-the-art LLM show that, while the model correctly identifies the high-level strategy in 84 % of cases, full identification-specification correctness drops to only 30 %, revealing that the bottleneck lies in the nuanced details of research design rather than in computation. CausalReasoningBenchmark is publicly available on Hugging Face and is designed to foster the development of more robust automated causal-inference systems.

Delayed outcomes are ubiquitous in online experimentation: treatment can affect whether an outcome occurs, when it occurs, and its realized value. To accommodate staggered entry while remaining robust to environmental nonstationarity and unit-level heterogeneity, we adopt a design-based perspective and target the sample cumulative reward in each arm as a function of calendar time. Our confidence sequences allow practitioners to continuously monitor the counterfactual incremental reward, such as revenue, that would have been realized by calendar time t had all entered units been assigned to treatment rather than control. The main technical challenge is the choice of design-based filtration, complicated by the presence of asynchronous potential outcome times. We show that the IPW treatment-effect estimation error is not a martingale with respect to any filtration, while each arm-specific IPW estimation error is a martingale with respect to a carefully chosen arm-specific event-time filtration. We therefore construct a confidence sequence for the treatment effect by combining two arm-level confidence sequences with a union bound, and further demonstrate that this can outperform the traditional design-based variance upper bound. Finally, we characterize the class of augmentations for which the per-arm AIPW estimation error remains a martingale.

Equation discovery aims to automate the discovery of scientific models in the form of mathematical equations from data. Technically, equation discovery is implemented by symbolic regression algorithms. Performance of symbolic regression for equation discovery is measured along two dimensions: Prediction accuracy on test data, and recovery of known groundtruth formulas. For standard regression, accuracy is typically measured on in-domain test data, for instance, by splitting a data set randomly into training and test data. While this makes sense for in-domain interpolation, which is the common goal in ordinary regression, it can be a misleading proxy for true model discovery and generalization. The obvious alternative is to measure out-of-domain accuracy. However, obtaining challenging out-of-domain test data is a non-trivial problem. Therefore, we focus on equation recovery for evaluating symbolic regression algorithms for equation discovery. The rationale is that symbolic regression algorithms that perform well in recovering known groundtruth formulas are good candidates to perform well in unknown equation discovery. Existing benchmarks for symbolic regression include equation recovery tasks, however, with only a small number of groundtruth formulas that are publicly known. Moreover, these benchmarks place less emphasis on evaluating the robustness of algorithms in terms of their behavior under changing dimensionality, sampling size, sampling distribution and sampling domain. This, however, is of central importance to practitioners wanting to discover equations for modeling natural phenomena, since data is almost certainly noisy and comes from diverse domains, distributions, and sample sizes. To fill this gap, we introduce the Equation Recovery Benchmark (ERBench), a new evaluation framework designed to rigorously assess algorithms explicitly targeting the task of equation discovery.

Improvements in language models are often driven by improving the quality of the data we train them on, which can be limiting when strong supervision is scarce. In this work, we show that paired preference data consisting of individually weak data points can enable gains beyond the strength of each individual data point. We formulate the delta learning hypothesis to explain this phenomenon, positing that the relative quality delta between points suffices to drive learning via preference tuning--even when supervised finetuning on the weak data hurts. We validate our hypothesis in controlled experiments and at scale, where we post-train 8B models on preference data generated by pairing a small 3B model's responses with outputs from an even smaller 1.5B model to create a meaningful delta. Strikingly, on a standard 11-benchmark evaluation suite (MATH, MMLU, etc.), our simple recipe matches the performance of Tulu 3, a state-of-the-art open model tuned from the same base model while relying on much stronger supervisors (e.g., GPT-4o). Thus, delta learning enables simpler and cheaper open recipes for state-of-the-art post-training. To better understand delta learning, we prove in logistic regression that the performance gap between two weak teacher models provides useful signal for improving a stronger student. Overall, our work shows that models can learn surprisingly well from paired data that might typically be considered weak.

Tabular machine learning presents a paradox: modern models achieve state-of-the-art performance using high-dimensional (high-D), collinear, error-prone data, defying the "Garbage In, Garbage Out" mantra. To help resolve this, we synthesize principles from Information Theory, Latent Factor Models, and Psychometrics, clarifying that predictive robustness arises not solely from data cleanliness, but from the synergy between data architecture and model capacity. Partitioning predictor-space "noise" into "Predictor Error" and "Structural Uncertainty" (informational deficits from stochastic generative mappings), we prove that leveraging high-D sets of error-prone predictors asymptotically overcomes both types of noise, whereas cleaning a low-D set is fundamentally bounded by Structural Uncertainty. We demonstrate why "Informative Collinearity" (dependencies from shared latent causes) enhances reliability and convergence efficiency, and explain why increased dimensionality reduces the latent inference burden, enabling feasibility with finite samples. To address practical constraints, we propose "Proactive Data-Centric AI" to identify predictors that enable robustness efficiently. We also derive boundaries for Systematic Error Regimes and show why models that absorb "rogue" dependencies can mitigate assumption violations. Linking latent architecture to Benign Overfitting, we offer a first step towards a unified view of robustness to Outcome Error and predictor-space noise, while also delineating when traditional DCAI's focus on label cleaning remains powerful. By redefining data quality from item-level perfection to portfolio-level architecture, we provide a theoretical rationale for "Local Factories" -- learning from live, uncurated enterprise "data swamps" -- supporting a deployment paradigm shift from "Model Transfer" to "Methodology Transfer'' to overcome static generalizability limitations.

Spurious correlations allow flexible models to predict well during training but poorly on related test distributions. Recent work has shown that models that satisfy particular independencies involving correlation-inducing nuisance variables have guarantees on their test performance. Enforcing such independencies requires nuisances to be observed during training. However, nuisances, such as demographics or image background labels, are often missing. Enforcing independence on just the observed data does not imply independence on the entire population. Here we derive mmd estimators used for invariance objectives under missing nuisances. On simulations and clinical data, optimizing through these estimates achieves test performance similar to using estimators that make use of the full data.

This study addresses the challenge of estimating average treatment effects (ATEs) for advertising campaigns in online marketplaces where complete randomized experimentation is infeasible. We propose two key innovations: (1) a shrinkage estimator that optimally combines observational and experimental data without assuming smooth treatment effects across campaigns, and (2) a Bayesian adaptive experimental design framework that efficiently selects campaigns for randomized evaluation that minimizes cumulative risk. Our shrinkage estimator achieves lower risk compared to existing methods by balancing bias-variance tradeoffs, while our adaptive design significantly reduces the costs of campaign randomization. We establish theoretical guarantees including asymptotic normality and regret bounds. In an application to Amazon Ads data analyzing 2,583 campaigns, our approach achieves equivalent estimation precision while requiring only half of the randomized experiments needed by random sampling, the standard method widely used in practice today. The proposed method serves as a practical solution for marketplace platforms to efficiently measure advertising effectiveness while managing experimentation costs.

Supervised learning datasets may contain multiple cues that explain the training set equally well, i.e., learning any of them would lead to the correct predictions on the training data. However, many of them can be spurious, i.e., lose their predictive power under a distribution shift and consequently fail to generalize to out-of-distribution (OOD) data. Recently developed "diversification" methods (Lee et al., 2023; Pagliardini et al., 2023) approach this problem by finding multiple diverse hypotheses that rely on different features. This paper aims to study this class of methods and identify the key components contributing to their OOD generalization abilities. We show that (1) diversification methods are highly sensitive to the distribution of the unlabeled data used for diversification and can underperform significantly when away from a method-specific sweet spot. (2) Diversification alone is insufficient for OOD generalization. The choice of the used learning algorithm, e.g., the model's architecture and pretraining, is crucial. In standard experiments (classification on Waterbirds and Office-Home datasets), using the second-best choice leads to an up to 20\% absolute drop in accuracy. (3) The optimal choice of learning algorithm depends on the unlabeled data and vice versa i.e. they are co-dependent. (4) Finally, we show that, in practice, the above pitfalls cannot be alleviated by increasing the number of diverse hypotheses, the major feature of diversification methods. These findings provide a clearer understanding of the critical design factors influencing the OOD generalization abilities of diversification methods. They can guide practitioners in how to use the existing methods best and guide researchers in developing new, better ones.

Over the broad landscape of experimental design, regression has been a powerful tool to accurately predict the outcome metrics of a system or model given a set of parameters, but has been traditionally restricted to methods which are only applicable to a specific task. In this paper, we propose OmniPred, a framework for training language models as universal end-to-end regressors over (x,y) evaluation data from diverse real world experiments. Using data sourced from Google Vizier, one of the largest blackbox optimization databases in the world, our extensive experiments demonstrate that through only textual representations of mathematical parameters and values, language models are capable of very precise numerical regression, and if given the opportunity to train over multiple tasks, can significantly outperform traditional regression models.

A key challenge in machine learning is to explain how learning dynamics select among the many solutions that achieve identical loss values in overparameterized models - a phenomenon known as implicit bias. Controlling this bias provides a direct mechanism on learned representations, which are central to interpretability, robustness, and reasoning in modern AI systems. Yet, despite its importance, existing explanations remain largely ad hoc and lack a unifying mechanism. We develop a theoretical and constructive framework in which implicit bias emerges as a geometric correction induced by the interplay between gradient noise and continuous symmetries of the loss. We compute the induced bias across a range of architectures, predicting new behaviors and explaining known ones. The approach also enables inverse design: by engineering predictor - preserving parameterizations, it is possible to shape the bias, with sparsity and spectral sparsity emerging as canonical instances. Numerical experiments support the theory and validate the inverse - design framework in controlled settings.

Can we build continuous generative models which generalize across scales, can be evaluated at any coordinate, admit calculation of exact derivatives, and are conceptually simple? Existing MLP-based architectures generate worse samples than the grid-based generators with favorable convolutional inductive biases. Models that focus on generating images at different scales do better, but employ complex architectures not designed for continuous evaluation of images and derivatives. We take a signal-processing perspective and treat continuous image generation as interpolation from samples. Indeed, correctly sampled discrete images contain all information about the low spatial frequencies. The question is then how to extrapolate the spectrum in a data-driven way while meeting the above design criteria. Our answer is FunkNN -- a new convolutional network which learns how to reconstruct continuous images at arbitrary coordinates and can be applied to any image dataset. Combined with a discrete generative model it becomes a functional generator which can act as a prior in continuous ill-posed inverse problems. We show that FunkNN generates high-quality continuous images and exhibits strong out-of-distribution performance thanks to its patch-based design. We further showcase its performance in several stylized inverse problems with exact spatial derivatives.

Recent advances in reinforcement learning (RL) have led to substantial improvements in the mathematical reasoning abilities of LLMs, as measured by standard benchmarks. Yet these gains often persist even when models are trained with flawed signals, such as random or inverted rewards. This raises a fundamental question: do such improvements reflect genuine reasoning, or are they merely artifacts of overfitting to benchmark-specific patterns? To answer this question, we adopt an evaluation-centric perspective and highlight two critical shortcomings in existing protocols. First, benchmark contamination arises because test problems are publicly available, thereby increasing the risk of data leakage. Second, evaluation fragility results from reliance on single-instance assessments, which are sensitive to stochastic outputs and fail to capture reasoning consistency. These limitations suggest the need for a new evaluation paradigm that can probe reasoning ability beyond memorization and one-off success. As response, we propose VAR-MATH, a symbolic evaluation framework that converts fixed numerical problems into parameterized templates and requires models to solve multiple instantiations of each. This design enforces consistency across structurally equivalent variants, mitigates contamination, and enhances robustness through bootstrapped metrics. We apply VAR-MATH to transform three popular benchmarks, AMC23, AIME24, and AIME25, into their symbolic counterparts, VAR-AMC23, VAR-AIME24, and VAR-AIME25. Experimental results show substantial performance drops for RL-trained models on these variabilized benchmarks, especially for smaller models, with average declines of 47.9\% on AMC23, 58.8\% on AIME24, and 72.9\% on AIME25. These findings indicate that some existing RL methods rely on superficial heuristics and fail to generalize beyond specific numerical forms.

Conformal prediction is a technique for constructing prediction intervals that attain valid coverage in finite samples, without making distributional assumptions. Despite this appeal, existing conformal methods can be unnecessarily conservative because they form intervals of constant or weakly varying length across the input space. In this paper we propose a new method that is fully adaptive to heteroscedasticity. It combines conformal prediction with classical quantile regression, inheriting the advantages of both. We establish a theoretical guarantee of valid coverage, supplemented by extensive experiments on popular regression datasets. We compare the efficiency of conformalized quantile regression to other conformal methods, showing that our method tends to produce shorter intervals.

Data augmentation is becoming essential for improving regression performance in critical applications including manufacturing, climate prediction, and finance. Existing techniques for data augmentation largely focus on classification tasks and do not readily apply to regression tasks. In particular, the recent Mixup techniques for classification have succeeded in improving the model performance, which is reasonable due to the characteristics of the classification task, but has limitations in regression. We show that mixing examples that have large data distances using linear interpolations may have increasingly-negative effects on model performance. Our key idea is thus to limit the distances between examples that are mixed. We propose RegMix, a data augmentation framework for regression that learns for each example how many nearest neighbors it should be mixed with for the best model performance using a validation set. Our experiments conducted both on synthetic and real datasets show that RegMix outperforms state-of-the-art data augmentation baselines applicable to regression.

Closed-loop decision-making systems (e.g., lending, screening, or recidivism risk assessment) often operate under fairness and service constraints while inducing feedback effects: decisions change who appears in the future, yielding non-stationary data and potentially amplifying disparities. We study online learning of a one-dimensional threshold policy from bandit feedback under demographic parity (DP) and, optionally, service-rate constraints. The learner observes only a scalar score each round and selects a threshold; reward and constraint residuals are revealed only for the chosen threshold. We propose Optimistic Feasible Search (OFS), a simple grid-based method that maintains confidence bounds for reward and constraint residuals for each candidate threshold. At each round, OFS selects a threshold that appears feasible under confidence bounds and, among those, maximizes optimistic reward; if no threshold appears feasible, OFS selects the threshold minimizing optimistic constraint violation. This design directly targets feasible high-utility thresholds and is particularly effective for low-dimensional, interpretable policy classes where discretization is natural. We evaluate OFS on (i) a synthetic closed-loop benchmark with stable contraction dynamics and (ii) two semi-synthetic closed-loop benchmarks grounded in German Credit and COMPAS, constructed by training a score model and feeding group-dependent acceptance decisions back into population composition. Across all environments, OFS achieves higher reward with smaller cumulative constraint violation than unconstrained and primal-dual bandit baselines, and is near-oracle relative to the best feasible fixed threshold under the same sweep procedure. Experiments are reproducible and organized with double-blind-friendly relative outputs.

On-policy distillation (OPD) trains a student on its own responses with token-level feedback from a stronger teacher, yet the teacher can fail on questions the student already answers correctly, and how often each model succeeds varies across tasks. OPD ignores these outcomes and, on average, pushes down even the student's correct responses; gating feedback by student correctness fixes the direction but uses the teacher in the same way whether or not it succeeded. We introduce DuoOPD, in which the student's outcome sets the direction of feedback and the joint teacher-student outcome decides how the teacher supports it: when only the teacher succeeds, its verified answer becomes context for scoring the student's failed response, and when only the student succeeds, a weight shared within the task reinforces the whole response. A single rule covers all four outcome combinations without task-specific settings. Across Qwen3 and Llama, DuoOPD outperforms all five baselines in mean macro accuracy, improving over OPD by 2.58 and 5.98 percentage points, and it also leads on two further task mixtures spanning scientific calculation, instruction following, and code generation. Ablations show that outcome-based direction alone stays near the gated baseline, while the joint-outcome designs supply most of the gain.

Safety performance evaluation is critical for developing and deploying connected and automated vehicles (CAVs). One prevailing way is to design testing scenarios using prior knowledge of CAVs, test CAVs in these scenarios, and then evaluate their safety performances. However, significant differences between CAVs and prior knowledge could severely reduce the evaluation efficiency. Towards addressing this issue, most existing studies focus on the adaptive design of testing scenarios during the CAV testing process, but so far they cannot be applied to high-dimensional scenarios. In this paper, we focus on the adaptive safety performance evaluation by leveraging the testing results, after the CAV testing process. It can significantly improve the evaluation efficiency and be applied to high-dimensional scenarios. Specifically, instead of directly evaluating the unknown quantity (e.g., crash rates) of CAV safety performances, we evaluate the differences between the unknown quantity and known quantity (i.e., control variates). By leveraging the testing results, the control variates could be well designed and optimized such that the differences are close to zero, so the evaluation variance could be dramatically reduced for different CAVs. To handle the high-dimensional scenarios, we propose the sparse control variates method, where the control variates are designed only for the sparse and critical variables of scenarios. According to the number of critical variables in each scenario, the control variates are stratified into strata and optimized within each stratum using multiple linear regression techniques. We justify the proposed method's effectiveness by rigorous theoretical analysis and empirical study of high-dimensional overtaking scenarios.

We employ random matrix theory to establish consistency of generalized cross validation (GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling efficient and consistent tuning of regularization and sketching parameters. Our results hold for a broad class of asymptotically free sketches under very mild data assumptions. For squared prediction risk, we provide a decomposition into an unsketched equivalent implicit ridge bias and a sketching-based variance, and prove that the risk can be globally optimized by only tuning sketch size in infinite ensembles. For general subquadratic prediction risk functionals, we extend GCV to construct consistent risk estimators, and thereby obtain distributional convergence of the GCV-corrected predictions in Wasserstein-2 metric. This in particular allows construction of prediction intervals with asymptotically correct coverage conditional on the training data. We also propose an "ensemble trick" whereby the risk for unsketched ridge regression can be efficiently estimated via GCV using small sketched ridge ensembles. We empirically validate our theoretical results using both synthetic and real large-scale datasets with practical sketches including CountSketch and subsampled randomized discrete cosine transforms.

This paper presents a data-driven, task-specific paradigm for experimental design, to shorten acquisition time, reduce costs, and accelerate the deployment of imaging devices. Current approaches in experimental design focus on model-parameter estimation and require specification of a particular model, whereas in imaging, other tasks may drive the design. Furthermore, such approaches often lead to intractable optimization problems in real-world imaging applications. Here we present a new paradigm for experimental design that simultaneously optimizes the design (set of image channels) and trains a machine-learning model to execute a user-specified image-analysis task. The approach obtains data densely-sampled over the measurement space (many image channels) for a small number of acquisitions, then identifies a subset of channels of prespecified size that best supports the task. We propose a method: TADRED for TAsk-DRiven Experimental Design in imaging, to identify the most informative channel-subset whilst simultaneously training a network to execute the task given the subset. Experiments demonstrate the potential of TADRED in diverse imaging applications: several clinically-relevant tasks in magnetic resonance imaging; and remote sensing and physiological applications of hyperspectral imaging. Results show substantial improvement over classical experimental design, two recent application-specific methods within the new paradigm, and state-of-the-art approaches in supervised feature selection. We anticipate further applications of our approach. Code is available: https://github.com/sbb-gh/experimental-design-multichannel

Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem that arises across fields such as mechanical engineering to aerospace engineering. Inverse design is typically formulated as an optimization problem, with recent works leveraging optimization across learned dynamics models. However, as models are optimized they tend to fall into adversarial modes, preventing effective sampling. We illustrate that by instead optimizing over the learned energy function captured by the diffusion model, we can avoid such adversarial examples and significantly improve design performance. We further illustrate how such a design system is compositional, enabling us to combine multiple different diffusion models representing subcomponents of our desired system to design systems with every specified component. In an N-body interaction task and a challenging 2D multi-airfoil design task, we demonstrate that by composing the learned diffusion model at test time, our method allows us to design initial states and boundary shapes that are more complex than those in the training data. Our method generalizes to more objects for N-body dataset and discovers formation flying to minimize drag in the multi-airfoil design task. Project website and code can be found at https://github.com/AI4Science-WestlakeU/cindm.

Models trained with counterfactually augmented data learn representations of the causal structure of tasks, enabling robust generalization. However, high-quality counterfactual data is scarce for most tasks and not easily generated at scale. When crowdsourced, such data is typically limited in scale and diversity; when generated using supervised methods, it is computationally expensive to extend to new counterfactual dimensions. In this work, we introduce DISCO (DIStilled COunterfactual Data), a new method for automatically generating high quality counterfactual data at scale. DISCO engineers prompts to generate phrasal perturbations with a large general language model. Then, a task-specific teacher model filters these generations to distill high-quality counterfactual data. While task-agnostic, we apply our pipeline to the task of natural language inference (NLI) and find that on challenging evaluations such as the NLI stress test, comparatively smaller student models trained with DISCO generated counterfactuals are more robust (6% absolute) and generalize better across distributions (2%) compared to models trained without data augmentation. Furthermore, DISCO augmented models are 10% more consistent between counterfactual pairs on three evaluation sets, demonstrating that DISCO augmentation enables models to more reliably learn causal representations. Our repository is available at: https://github.com/eric11eca/disco

We study the optimisation problem associated with Gaussian process regression using squared loss. The most common approach to this problem is to apply an exact solver, such as conjugate gradient descent, either directly, or to a reduced-order version of the problem. Recently, driven by successes in deep learning, stochastic gradient descent has gained traction as an alternative. In this paper, we show that when done rightx2014by which we mean using specific insights from the optimisation and kernel communitiesx2014this approach is highly effective. We thus introduce a particular stochastic dual gradient descent algorithm, that may be implemented with a few lines of code using any deep learning framework. We explain our design decisions by illustrating their advantage against alternatives with ablation studies and show that the new method is highly competitive. Our evaluations on standard regression benchmarks and a Bayesian optimisation task set our approach apart from preconditioned conjugate gradients, variational Gaussian process approximations, and a previous version of stochastic gradient descent for Gaussian processes. On a molecular binding affinity prediction task, our method places Gaussian process regression on par in terms of performance with state-of-the-art graph neural networks.

This paper studies a machine learning regression problem as a multivariate approximation problem using the framework of the theory of random functions. An ab initio derivation of a regression method is proposed, starting from postulates of indifference. It is shown that if a probability measure on an infinite-dimensional function space possesses natural symmetries (invariance under translation, rotation, scaling, and Gaussianity), then the entire solution scheme, including the kernel form, the type of regularization, and the noise parameterization, follows analytically from these postulates. The resulting kernel coincides with a generalized polyharmonic spline; however, unlike existing approaches, it is not chosen empirically but arises as a consequence of the indifference principle. This result provides a theoretical foundation for a broad class of smoothing and interpolation methods, demonstrating their optimality in the absence of a priori information.

The inherent rigidity of fixed-size benchmarks makes them an inefficient tool for model evaluation. Diverse evaluation objectives, including model ranking, model selection and testing throughout development, demand varying levels of statistical power. The mismatch between fixed sample sizes and these diverse needs results in either excessive computational cost or compromised reliability - a critical concern for model evaluation. To overcome these limitations, we call for adoption of sequential testing in our field. We provide an adaptive evaluation framework, that provides a principled way to navigate the trade-off between efficiency and reliability in model evaluation. Our framework combines the established statistical paradigm of sequential testing with stopping criteria tailored to common evaluation needs such as diminishing returns detection, and minimum detectable effect size. We demonstrate its ability to adaptively manage the efficiency-reliability trade-off on the Open VLM Leaderboard, including, for example, a 80% reduction in computational cost compared to fixed-size evaluation (with a 2.5-point CI width allowance) while maintaining statistical significance.

Denoising diffusion probabilistic models (DDPMs) (Ho et al. 2020) have shown impressive results on image and waveform generation in continuous state spaces. Here, we introduce Discrete Denoising Diffusion Probabilistic Models (D3PMs), diffusion-like generative models for discrete data that generalize the multinomial diffusion model of Hoogeboom et al. 2021, by going beyond corruption processes with uniform transition probabilities. This includes corruption with transition matrices that mimic Gaussian kernels in continuous space, matrices based on nearest neighbors in embedding space, and matrices that introduce absorbing states. The third allows us to draw a connection between diffusion models and autoregressive and mask-based generative models. We show that the choice of transition matrix is an important design decision that leads to improved results in image and text domains. We also introduce a new loss function that combines the variational lower bound with an auxiliary cross entropy loss. For text, this model class achieves strong results on character-level text generation while scaling to large vocabularies on LM1B. On the image dataset CIFAR-10, our models approach the sample quality and exceed the log-likelihood of the continuous-space DDPM model.

Recent progress in large language model (LLM) agents has largely focused on embedding self-improvement mechanisms inside the agent or searching over many concurrent variants. While these approaches can raise aggregate scores, they often yield unstable and hard-to-audit improvement trajectories, making it difficult to guarantee non-regression or to reason about failures across versions. We reframe agent improvement as release engineering: agents are treated as shippable artifacts, and improvement is externalized into a regression-aware release pipeline. We introduce AgentDevel, a release engineering pipeline that iteratively runs the current agent, produces implementation-blind, symptom-level quality signals from execution traces, synthesizes a single release candidate (RC) via executable diagnosis, and promotes it under flip-centered gating. AgentDevel features three core designs: (i) an implementation-blind LLM critic that characterizes failure appearances without accessing agent internals, (ii) script-based executable diagnosis that aggregates dominant symptom patterns and produces auditable engineering specifications, and (iii) flip-centered gating that prioritizes pass to fail regressions and fail to pass fixes as first-class evidence. Unlike population-based search or in-agent self-refinement, AgentDevel maintains a single canonical version line and emphasizes non-regression as a primary objective. Experiments on execution-heavy benchmarks demonstrate that AgentDevel yields stable improvements with significantly fewer regressions while producing reproducible, auditable artifacts. Overall, AgentDevel provides a practical development discipline for building, debugging, and releasing LLM agents as software development.

Data attribution seeks to trace model outputs back to training data. With the recent development of diffusion models, data attribution has become a desired module to properly assign valuations for high-quality or copyrighted training samples, ensuring that data contributors are fairly compensated or credited. Several theoretically motivated methods have been proposed to implement data attribution, in an effort to improve the trade-off between computational scalability and effectiveness. In this work, we conduct extensive experiments and ablation studies on attributing diffusion models, specifically focusing on DDPMs trained on CIFAR-10 and CelebA, as well as a Stable Diffusion model LoRA-finetuned on ArtBench. Intriguingly, we report counter-intuitive observations that theoretically unjustified design choices for attribution empirically outperform previous baselines by a large margin, in terms of both linear datamodeling score and counterfactual evaluation. Our work presents a significantly more efficient approach for attributing diffusion models, while the unexpected findings suggest that at least in non-convex settings, constructions guided by theoretical assumptions may lead to inferior attribution performance. The code is available at https://github.com/sail-sg/D-TRAK.

Real-world regression often exhibits shortcuts: attributes that are spuriously correlated with continuous targets in training, yet unreliable under deployment shifts; regressing targets using such shortcuts may fail catastrophically at test time. Existing studies on spurious correlations focus primarily on classification, where labels are categorical and groups are naturally defined. However, many real-world tasks require continuous prediction, where hard label boundaries or discrete group-label pairs do not exist. We define Deep Spurious Regression (DSR) as learning from regression data with attribute-label confounding, addressing continuous spurious correlations, and generalizing to all attribute-label combinations at test time. Motivated by the intrinsic difference between classification and regression shortcuts, we propose to exploit the similarity among spurious attributes in both label and feature spaces, thereby accounting for nearby targets and related groups while calibrating both label and learned feature distributions across attributes. Extensive experiments on common real-world DSR datasets that span computer vision, environmental sensing, and large language model (LLM) regression verify the superior performance of our strategies. Our work fills the gap in benchmarks and techniques for studying spurious correlations in continuous prediction.

Machine learning models trained on Earth observation data, such as satellite imagery, have demonstrated significant promise in predicting household-level wealth indices, enabling the creation of high-resolution wealth maps that can be leveraged across multiple causal trials. However, because standard training objectives prioritize overall predictive accuracy, these predictions inherently suffer from shrinkage toward the mean, leading to attenuated estimates of causal treatment effects and limiting their utility in policy. Existing debiasing methods, such as Prediction-Powered Inference, can handle this attenuation bias but require additional fresh ground-truth data at the downstream stage of causal inference, which restricts their applicability in data-scarce environments. Here, we introduce and evaluate two correction methods -- linear calibration correction and Tweedie's correction -- that substantially reduce prediction bias without relying on newly collected labeled data. Linear calibration corrects bias through a straightforward linear transformation derived from held-out calibration data, whereas Tweedie's correction leverages empirical Bayes principles to directly address shrinkage-induced biases by exploiting score functions derived from the model's learning patterns. Through analytical exercises and experiments using Demographic and Health Survey data, we demonstrate that the proposed methods meet or outperform existing approaches that either require (a) adjustments to training pipelines or (b) additional labeled data. These approaches may represent a promising avenue for improving the reliability of causal inference when direct outcome measures are limited or unavailable, enabling a "one map, many trials" paradigm where a single upstream data creation team produces predictions usable by many downstream teams across diverse ML pipelines.

Graphic layouts serve as an important and engaging medium for visual communication across different channels. While recent layout generation models have demonstrated impressive capabilities, they frequently fail to align with nuanced human aesthetic judgment. Existing preference datasets and reward models trained on text-to-image generation do not generalize to layout evaluation, where the spatial arrangement of identical elements determines quality. To address this critical gap, we introduce DesignSense-10k, a large-scale dataset of 10,235 human-annotated preference pairs for graphic layout evaluation. We propose a five-stage curation pipeline that generates visually coherent layout transformations across diverse aspect ratios, using semantic grouping, layout prediction, filtering, clustering, and VLM-based refinement to produce high-quality comparison pairs. Human preferences are annotated using a 4-class scheme (left, right, both good, both bad) to capture subjective ambiguity. Leveraging this dataset, we train DesignSense, a vision-language model-based classifier that substantially outperforms existing open-source and proprietary models across comprehensive evaluation metrics (54.6% improvement in Macro F1 over the strongest proprietary baseline). Our analysis shows that frontier VLMs remain unreliable overall and fail catastrophically on the full four-class task, underscoring the need for specialized, preference-aware models. Beyond the dataset, our reward model DesignSense yields tangible downstream gains in layout generation. Using our judge during RL based training improves generator win rate by about 3%, while inference-time scaling, which involves generating multiple candidates and selecting the best one, provides a 3.6% improvement. These results highlight the practical impact of specialized, layout-aware preference modeling on real-world layout generation quality.

The phenomenon of model-wise double descent, where the test error peaks and then reduces as the model size increases, is an interesting topic that has attracted the attention of researchers due to the striking observed gap between theory and practice Belkin2018ReconcilingMM. Additionally, while double descent has been observed in various tasks and architectures, the peak of double descent can sometimes be noticeably absent or diminished, even without explicit regularization, such as weight decay and early stopping. In this paper, we investigate this intriguing phenomenon from the optimization perspective and propose a simple optimization-based explanation for why double descent sometimes occurs weakly or not at all. To the best of our knowledge, we are the first to demonstrate that many disparate factors contributing to model-wise double descent (initialization, normalization, batch size, learning rate, optimization algorithm) are unified from the viewpoint of optimization: model-wise double descent is observed if and only if the optimizer can find a sufficiently low-loss minimum. These factors directly affect the condition number of the optimization problem or the optimizer and thus affect the final minimum found by the optimizer, reducing or increasing the height of the double descent peak. We conduct a series of controlled experiments on random feature models and two-layer neural networks under various optimization settings, demonstrating this optimization-based unified view. Our results suggest the following implication: Double descent is unlikely to be a problem for real-world machine learning setups. Additionally, our results help explain the gap between weak double descent peaks in practice and strong peaks observable in carefully designed setups.

Calibrated uncertainty estimates in machine learning are crucial to many fields such as autonomous vehicles, medicine, and weather and climate forecasting. While there is extensive literature on uncertainty calibration for classification, the classification findings do not always translate to regression. As a result, modern models for predicting uncertainty in regression settings typically produce uncalibrated and overconfident estimates. To address these gaps, we present a calibration method for regression settings that does not assume a particular uncertainty distribution over the error: Calibrating Regression Uncertainty Distributions Empirically (CRUDE). CRUDE makes the weaker assumption that error distributions have a constant arbitrary shape across the output space, shifted by predicted mean and scaled by predicted standard deviation. We detail a theoretical connection between CRUDE and conformal inference. Across an extensive set of regression tasks, CRUDE demonstrates consistently sharper, better calibrated, and more accurate uncertainty estimates than state-of-the-art techniques.

We propose a computationally efficient inferential procedure for longitudinal function-on-function regression. The method follows a marginal three-step approach: (1) fit massive pointwise longitudinal scalar-on-function regression models, (2) smooth the resulting estimates along the bivariate functional domain, and (3) compute confidence bands using either an analytic approach for Gaussian data or a cluster bootstrap for Gaussian or non-Gaussian data. Simulation studies demonstrate that the proposed method achieves accurate estimation and valid inference, while substantially reducing computational burden compared to existing approaches. Methods are motivated by a physical activity intervention trial in older adults where high-dimensional wearable data were collected longitudinally across multiple visits. Our applications reveal significant increases in physical activity in the morning using interpersonal intervention strategies, but not intrapersonal strategies. The proposed methods are implemented in an R package.

Neural surrogates promise large speedups over classical solvers for physical dynamics but fail silently at sharp dynamical events such as shocks, fronts, and contact. We present hybrid neural world models for physical dynamics: a recipe for training and deploying multi-horizon surrogates in physical state space, where a single network with continuous horizon conditioning is trained with direct supervision against textbook reference solvers to predict any future state at horizon T in one forward pass. Although no part of the training data, loss function, or architecture supervises discontinuity location, the trained surrogate encodes it implicitly, recoverable from its forward passes alone as a per-trajectory error map that concentrates on shocks, fronts, and contacts, and stays small elsewhere. The map is competitive with or better than standard label-free baselines including deep ensembles, learned error heads, gradient-magnitude indicators, and locally-adaptive conformal prediction, while using only a single trained network and requiring no calibration set or governing-equation knowledge. The recipe supports two operating points. Mode 1 runs the surrogate alone for maximum throughput, with same-hardware CPU speedups of 26x to 72x against textbook solvers on the PDE environments. Mode 2 uses the error map to gate a reference-solver fallback, deferring uncertain trajectories and roughly halving the surrogate's residual error at the default operating point. The recipe applies without modification across reaction-diffusion, compressible Euler, and rigid-body collision dynamics.

Efficiently and flexibly estimating treatment effect heterogeneity is an important task in a wide variety of settings ranging from medicine to marketing, and there are a considerable number of promising conditional average treatment effect estimators currently available. These, however, typically rely on the assumption that the measured covariates are enough to justify conditional exchangeability. We propose the P-learner, motivated by the R- and DR-learner, a tailored two-stage loss function for learning heterogeneous treatment effects in settings where exchangeability given observed covariates is an implausible assumption, and we wish to rely on proxy variables for causal inference. Our proposed estimator can be implemented by off-the-shelf loss-minimizing machine learning methods, which in the case of kernel regression satisfies an oracle bound on the estimated error as long as the nuisance components are estimated reasonably well.

Training a large and state-of-the-art machine learning model typically necessitates the use of large-scale datasets, which, in turn, makes the training and parameter-tuning process expensive and time-consuming. Some researchers opt to distil information from real-world datasets into tiny and compact synthetic datasets while maintaining their ability to train a well-performing model, hence proposing a data-efficient method known as Dataset Distillation (DD). Despite recent progress in this field, existing methods still underperform and cannot effectively replace large datasets. In this paper, unlike previous methods that focus solely on improving the efficacy of student distillation, we are the first to recognize the important interplay between expert and student. We argue the significant impact of expert smoothness when employing more potent expert trajectories in subsequent dataset distillation. Based on this, we introduce the integration of clipping loss and gradient penalty to regulate the rate of parameter changes in expert trajectories. Furthermore, in response to the sensitivity exhibited towards randomly initialized variables during distillation, we propose representative initialization for synthetic dataset and balanced inner-loop loss. Finally, we present two enhancement strategies, namely intermediate matching loss and weight perturbation, to mitigate the potential occurrence of cumulative errors. We conduct extensive experiments on datasets of different scales, sizes, and resolutions. The results demonstrate that the proposed method significantly outperforms prior methods.

Observational studies require adjustment for confounding factors that are correlated with both the treatment and outcome. In the setting where the observed variables are tabular quantities such as average income in a neighborhood, tools have been developed for addressing such confounding. However, in many parts of the developing world, features about local communities may be scarce. In this context, satellite imagery can play an important role, serving as a proxy for the confounding variables otherwise unobserved. In this paper, we study confounder adjustment in this non-tabular setting, where patterns or objects found in satellite images contribute to the confounder bias. Using the evaluation of anti-poverty aid programs in Africa as our running example, we formalize the challenge of performing causal adjustment with such unstructured data -- what conditions are sufficient to identify causal effects, how to perform estimation, and how to quantify the ways in which certain aspects of the unstructured image object are most predictive of the treatment decision. Via simulation, we also explore the sensitivity of satellite image-based observational inference to image resolution and to misspecification of the image-associated confounder. Finally, we apply these tools in estimating the effect of anti-poverty interventions in African communities from satellite imagery.

In engineering design, navigating complex decision-making landscapes demands a thorough exploration of the design, performance, and constraint spaces, often impeded by resource-intensive simulations. Data-driven methods can mitigate this challenge by harnessing historical data to delineate feasible domains, accelerate optimization, or evaluate designs. However, the implementation of these methods usually demands machine-learning expertise and multiple trials to choose the right method and hyperparameters. This makes them less accessible for numerous engineering situations. Additionally, there is an inherent trade-off between training speed and accuracy, with faster methods sometimes compromising precision. In our paper, we demonstrate that a recently released general-purpose transformer-based classification model, TabPFN, is both fast and accurate. Notably, it requires no dataset-specific training to assess new tabular data. TabPFN is a Prior-Data Fitted Network, which undergoes a one-time offline training across a broad spectrum of synthetic datasets and performs in-context learning. We evaluated TabPFN's efficacy across eight engineering design classification problems, contrasting it with seven other algorithms, including a state-of-the-art AutoML method. For these classification challenges, TabPFN consistently outperforms in speed and accuracy. It is also the most data-efficient and provides the added advantage of being differentiable and giving uncertainty estimates. Our findings advocate for the potential of pre-trained models that learn from synthetic data and require no domain-specific tuning to make data-driven engineering design accessible to a broader community and open ways to efficient general-purpose models valid across applications. Furthermore, we share a benchmark problem set for evaluating new classification algorithms in engineering design.