arXiv subjects

Larry Wasserman

Publications and source records attributed to Larry Wasserman.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Inference with Black-box Predictions

Powerful black-box predictive models have motivated many proposals for combining observed data with predictions to perform valid statistical inference. Despite this progress, the field lacks a unifying principle that explains how hypothesis tests should integrate data and predictions in a way that is both valid and efficient. In this work, we address this gap in the high-dimensional Gaussian sequence model. We characterize the information-theoretic limits of inference with black-box predictions when their accuracies are known and, for orthogonal predictions, when they are unknown. Building on these characterizations, we develop practical hypothesis tests that adapt to the unknown accuracies of the predictions while benefiting from strong alignment among them.

math.ST↗

arXiv2026

Wasserstein Parallel Transport for Predicting the Dynamics of Statistical Systems

Many scientific systems, such as cellular populations or economic cohorts, are naturally described by probability distributions that evolve over time. Predicting how such a system would have evolved under different forces or initial conditions is fundamental to causal inference, domain adaptation, and counterfactual prediction. However, the space of distributions often lacks the vector space structure on which classical methods rely. To address this, we introduce a general notion of parallel dynamics at a distributional level. We base this principle on parallel transport of tangent dynamics along optimal transport geodesics and call it ``Wasserstein Parallel Trends''. By replacing the vector subtraction of classic methods with geodesic parallel transport, we can provide counterfactual comparisons of distributional dynamics in applications such as causal inference, domain adaptation, and batch-effect correction in experimental settings. The main mathematical contribution is a novel notion of fanning scheme on the Wasserstein manifold that allows us to efficiently approximate parallel transport along geodesics while also providing the first theoretical guarantees for parallel transport in the Wasserstein space. We also show that Wasserstein Parallel Trends recovers the classic parallel trends assumption for averages as a special case and derive closed-form parallel transport for Gaussian measures. We deploy the method on synthetic data and two single-cell RNA sequencing datasets to impute gene-expression dynamics across biological systems.

stat.ML↗

arXiv2026

Distributional Discontinuity Design

Regression discontinuity and kink designs are typically analyzed through mean effects, even when treatment changes the shape of the entire outcome distribution. To address this, we introduce distributional discontinuity designs, a framework for estimating causal effects for a scalar outcome at the boundary of a discontinuity in treatment assignment. Our estimand is the Wasserstein distance between limiting conditional outcome distributions; a single scale-interpretable measure of distribution shift. We show that this weakly bounds the average treatment effect, where equality holds if and only if the treatment effect is purely additive; thus, departure from equality measures effect heterogeneity. To further encode effect heterogeneity we show that the Wasserstein distance admits an orthogonal decomposition into squared differences in $L$-moments, thereby quantifying the contribution from location, scale, skewness, and higher-order shape components to the overall distributional distance. Next, we extend this framework to distributional kink designs by evaluating the Wasserstein derivative at a policy kink; this describes the flow of probability mass through the kink. In the case of fuzzy kink designs, we derive new identification results. Finally, we apply our methods on real data by re-analyzing two natural experiments to compare our distributional effects to traditional causal estimands.

stat.ME↗

arXiv2025

Machine Learning-based Unfolding for Cross Section Measurements in the Presence of Nuisance Parameters

Statistically correcting measured cross sections for detector effects is an important step across many applications. In particle physics, this inverse problem is known as unfolding. In cases with complex instruments, the distortions they introduce are often known only implicitly through simulations of the detector. Modern machine learning has enabled efficient simulation-based approaches for unfolding high-dimensional data. Among these, one of the first methods successfully deployed on experimental data is the OmniFold algorithm, a classifier-based Expectation-Maximization procedure. In practice, however, the forward model is only approximately specified, and the corresponding uncertainty is encoded through nuisance parameters. Building on the well-studied OmniFold algorithm, we show how to extend machine learning-based unfolding to incorporate nuisance parameters. Our new algorithm, called Profile OmniFold, is demonstrated using a Gaussian example as well as a particle physics case study using simulated data from the CMS Experiment at the Large Hadron Collider.

stat.AP↗

arXiv2025

Statistical Properties of Rectified Flow

Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these methods are scant. The rectified flow can be regarded as an approximation to optimal transport, but in contrast to other transport methods that require optimization over a function space, computing the rectified flow only requires standard statistical tools such as regression or density estimation, which we leverage to develop empirical versions of transport maps. We study some structural properties of the rectified flow, including existence, uniqueness, and regularity, as well as the related statistical properties, such as rates of convergence and central limit theorems, for some selected estimators. To do so, we analyze the bounded and unbounded cases separately as each presents unique challenges. In both cases, we are able to establish convergence at faster rates than those for the usual nonparametric regression and density estimation.

math.ST↗

arXiv2025

Testing Imprecise Hypotheses

Many scientific applications involve testing theories that are only partially specified. This task often amounts to testing the goodness-of-fit of a candidate distribution while allowing for reasonable deviations from it. The tolerant testing framework provides a systematic way of constructing such tests. Rather than testing the simple null hypothesis that data was drawn from a candidate distribution, a tolerant test assesses whether the data is consistent with any distribution that lies within a given neighborhood of the candidate. As this neighborhood grows, the tolerance to misspecification increases, while the power of the test decreases. In this work, we characterize the information-theoretic trade-off between the size of the neighborhood and the power of the test, in several canonical models. On the one hand, we characterize the optimal trade-off for tolerant testing in the Gaussian sequence model, under deviations measured in both smooth and non-smooth norms. On the other hand, we study nonparametric analogues of this problem in smooth regression and density models. Along the way, we establish the sub-optimality of the classical chi-squared statistic for tolerant testing, and study simple alternative hypothesis tests.

math.ST↗

arXiv2025

COWs and their Hybrids: A Statistical View of Custom Orthogonal Weights

A recurring challenge in high energy physics is inference of the signal component from a distribution for which observations are assumed to be a mixture of signal and background events. A standard assumption is that there exists information encoded in a discriminant variable that is effective at separating signal and background. This can be used to assign a signal weight to each event, with these weights used in subsequent analyses of one or more control variables of interest. The custom orthogonal weights (COWs) approach of Dembinski, et al.(2022), a generalization of the sPlot approach of Barlow (1987) and Pivk and Le Diberder (2005), is tailored to address this objective. The problem, and this method, present interesting and novel statistical issues. Here we formalize the assumptions needed and the statistical properties, while also considering extensions and alternative approaches.

stat.AP↗

arXiv2025

Response Matrix Estimation in Unfolding Differential Cross Sections

The unfolding problem in particle physics is to make inferences about the true particle spectrum based on smeared observations from a detector. This is an ill-posed inverse problem, where small changes in the smeared distribution can lead to large fluctuations in the unfolded distribution. The forward operator is the response matrix which models the detector response. In practice, the forward operator is rarely known analytically and is instead estimated using Monte Carlo simulation. This raises the question of how to best estimate the response matrix and what impact this estimation has on the unfolded solutions. In most analyses at the LHC, response matrix estimation is done by binning the true and smeared events and counting the propagation of events between the bins. However, this approach can result in a noisy estimate of the response matrix, especially with a small Monte Carlo sample size. Unexpectedly, we also find that the noise in the estimated response matrix can inadvertently regularize the problem. As an alternative, we propose to estimate the response matrix through the use of conditional density estimation of the response kernel in the unbinned setting followed by binning this estimator. Using simulation studies, we investigate the performance of the two approaches.

hep-ex↗

arXiv2025

Causal Geodesy: Counterfactual Estimation Along the Path Between Correlation and Causation

We introduce causal geodesy, a framework for studying the landscape of stochastic interventions that lie between the two extremes of performing no intervention, and performing a sharp intervention that sets an exposure equal to a specific value. We define this framework by constructing paths of distributions that smoothly interpolate between the treatment density and a point mass at the target intervention. Thus, each path starts at a purely observational (or correlational) quantity and moves into a counterfactual world. Of particular interest are paths that correspond to geodesics in some metric, i.e. the shortest path. We then consider the interpretation and estimation of the corresponding causal effects as we move along the path from correlation toward causation.

stat.ME↗

arXiv2025

Robust Simulation Based Inference

Simulation-Based Inference (SBI) is an approach to statistical inference where simulations from an assumed model are used to construct estimators and confidence sets. SBI is often used when the likelihood is intractable and to construct confidence sets that do not rely on asymptotic methods or regularity conditions. Traditional SBI methods assume that the model is correct, but, as always, this can lead to invalid inference when the model is misspecified. This paper introduces robust methods that allow for valid frequentist inference in the presence of model misspecification. We propose a framework where the target of inference is a projection parameter that minimizes a discrepancy between the true distribution and the assumed model. The method guarantees valid inference, even when the model is incorrectly specified and even if the standard regularity conditions fail. Alternatively, we introduce model expansion through exponential tilting as another way to account for model misspecification. We also develop an SBI based goodness-of-fit test to detect model misspecification. Finally, we propose two ideas that are useful in the SBI framework beyond robust inference: an SBI based method to obtain closed form approximations of intractable models and an active learning approach to more efficiently sample the parameter space.

stat.ME↗

arXiv2025

Disentangled Feature Importance

When predictors are statistically dependent, the appropriate definition of feature importance depends on the operational goal. Conditional-incremental measures are well-suited for feature selection, acquisition, and compression, where shared predictive information is treated as redundancy. For post-hoc interpretation, however, the goal is often to attribute predictive signals across correlated measurement channels. We introduce Disentangled Feature Importance (DFI), a population-level attribution framework for this setting. DFI maps covariates to an independent latent representation under a specified entropic optimal transport geometry, computes latent importance, and attributes it back to the original covariates through barycentric sensitivities. We show that broad conditional-incremental FI functionals target conditional incremental predictive value under squared-error loss, and therefore answer a different question from attribution of shared predictive signal under dependence. Under fixed transport cost, reference law, and regularization level, DFI defines a well-specified family of estimands. Latent scores admit a functional ANOVA interpretation, and in the Gaussian linear case, the attributed DFI recovers the classical $R^2$ decomposition for correlated regressors. We derive influence-function-based inference under nuisance-rate and smoothness conditions, and show in simulations and an HIV-1 neutralization-resistance analysis that DFI yields stable, interpretable, uncertainty-quantified attributions of shared predictive signal.

stat.ML↗

arXiv2025

Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectives

In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified cost. In this paper we review recent advances in estimating and developing limit theorems for the OT map, using samples from the underlying distributions. We also review parallel lines of work that establish similar results for special cases and variants of the basic OT setup. We conclude with a discussion of key directions for future research with the goal of providing practitioners with reliable inferential tools.

math.ST↗

arXiv2025

Testing Random Effects for Binomial Data

In modern scientific research, small-scale studies with limited participants are increasingly common. However, interpreting individual outcomes can be challenging, making it standard practice to combine data across studies using random effects to draw broader scientific conclusions. In this work, we introduce an optimal methodology for assessing the goodness of fit of a reference distribution for the random effects arising from binomial counts. For meta-analyses, we also derive optimal tests to evaluate whether multiple studies are in agreement before pooling the data. In all cases, we prove that the proposed tests optimally distinguish null and alternative hypotheses separated in the 1-Wasserstein distance.

math.ST↗

arXiv2025

Active multiple testing with proxy p-values and e-values

Researchers often lack the resources to test every hypothesis of interest directly or compute test statistics comprehensively, but often possess auxiliary data from which we can compute an estimate of the experimental outcome. We introduce a novel approach for selecting which hypotheses to query a statistic (e.g., run an experiment, perform expensive computation, etc.) in a hypothesis testing setup by leveraging estimates to compute proxy statistics. Our framework allows a scientist to propose a proxy statistic and then query the true statistic with some probability based on the value of the proxy. We make no assumptions about how the proxy is derived, and it can be arbitrarily dependent on the true statistic. If the true statistic is not queried, the proxy is used in its place. We characterize "active" methods that produce valid p-values and e-values in this setting and utilize this framework in the multiple testing setting to create procedures with false discovery rate (FDR) control. Through simulations and real data analysis of causal effects in scCRISPR screen experiments, we empirically demonstrate that our proxy framework has both high power and low resource usage when our proxies are accurate estimates of the respective true statistics.

stat.ME↗

arXiv2024

Stochastic interventions, sensitivity analysis, and optimal transport

Recent methodological research in causal inference has focused on effects of stochastic interventions, which assign treatment randomly, often according to subject-specific covariates. In this work, we demonstrate that the usual notion of stochastic interventions have a surprising property: when there is unmeasured confounding, bounds on their effects do not collapse when the policy approaches the observational regime. As an alternative, we propose to study generalized policies, treatment rules that can depend on covariates, the natural value of treatment, and auxiliary randomness. We show that certain generalized policy formulations can resolve the "non-collapsing" bound issue: bounds narrow to a point when the target treatment distribution approaches that in the observed data. Moreover, drawing connections to the theory of optimal transport, we characterize generalized policies that minimize worst-case bound width in various sensitivity analysis models, as well as corresponding sharp bounds on their causal effects. These optimal policies are new, and can have a more parsimonious interpretation compared to their usual stochastic policy analogues. Finally, we develop flexible, efficient, and robust estimators for the sharp nonparametric bounds that emerge from the framework.

stat.ME↗

arXiv2024

Causal Inference Using Augmented Epidemic Models

Epidemic models describe the evolution of a communicable disease over time. These models are often modified to include the effects of interventions (control measures) such as vaccination, social distancing, school closings etc. Many such models were proposed during the COVID-19 epidemic. Inevitably these models are used to answer the question: What is the effect of the intervention on the epidemic? These models can either be interpreted as data generating models describing observed random variables or as causal models for counterfactual random variables. These two interpretations are often conflated in the literature. We discuss the difference between these two types of models, and then we discuss how to estimate the parameters of the model. Our focus is causal inference for parameters in epidemic models by adjusting for confounders, allowing time varying interventions.

stat.ME↗

arXiv2024

Assumption-Lean Post-Integrated Inference with Surrogate Control Outcomes

Data integration methods aim to extract low-dimensional embeddings from high-dimensional outcomes to remove unwanted variations, such as batch effects and unmeasured covariates, across heterogeneous datasets. However, multiple hypothesis testing after integration can be biased due to data-dependent processes. We introduce a robust post-integrated inference method that accounts for latent heterogeneity by utilizing control outcomes. Leveraging causal interpretations, we derive nonparametric identifiability of the direct effects using negative control outcomes. By utilizing surrogate control outcomes as an extension of negative control outcomes, we develop semiparametric inference on projected direct effect estimands, accounting for hidden mediators, confounders, and moderators. These estimands remain statistically meaningful under model misspecifications and with error-prone embeddings. We provide bias quantifications and finite-sample linear expansions with uniform concentration bounds. The proposed doubly robust estimators are consistent and efficient under minimal assumptions and potential misspecification, facilitating data-adaptive estimation with machine learning algorithms. Our proposal is evaluated using random forests through simulations and analysis of single-cell CRISPR perturbed datasets, which may contain potential unmeasured confounders.

stat.ME↗

arXiv2024

Multidimensional Deconvolution with Profiling

In many experimental contexts, it is necessary to statistically remove the impact of instrumental effects in order to physically interpret measurements. This task has been extensively studied in particle physics, where the deconvolution task is called unfolding. A number of recent methods have shown how to perform high-dimensional, unbinned unfolding using machine learning. However, one of the assumptions in all of these methods is that the detector response is correctly modeled in the Monte Carlo simulation. In practice, the detector response depends on a number of nuisance parameters that can be constrained with data. We propose a new algorithm called Profile OmniFold, which works in a similar iterative manner as the OmniFold algorithm while being able to simultaneously profile the nuisance parameters. We illustrate the method with a Gaussian example as a proof of concept highlighting its promising capabilities.

hep-ph↗