arXiv subjects

Sirui Lin

Publications and source records attributed to Sirui Lin.

7 recordsLinked to original sources

arXiv2026

Statistical Inference in Causal Partial Identification with Smooth Densities

Many causal quantities are only partially identifiable due to the inherent missingness of potential outcomes, and the associated partial identification (PI) sets can be obtained by solving an optimal transport (OT) problem. Covariates often provide additional information about the potential outcomes and thus yield tighter PI sets, which can be obtained via conditional optimal transport (COT). However, COT-based PI set estimators are susceptible to the curse of dimensionality in the covariates and outcomes, which precludes the asymptotic normality and hinders statistical inference. In this paper, we exploit smoothness in the marginal densities of covariates and potential outcomes and develop a wavelet-based primal method for COT with multivariate outcomes and covariates. Moreover, for quadratic cost functions, we establish a stability result for COT and prove asymptotic normality of the proposed estimator. This characterization of the asymptotic distribution enables valid statistical inference for the partial identification set. Empirically, we validate the estimation and inference performance of our approach through numerical experiments in comparison with existing benchmarks.

math.ST↗

arXiv2025

Causal Partial Identification via Conditional Optimal Transport

We study the estimation of causal estimand involving the joint distribution of treatment and control outcomes for a single unit. In typical causal inference settings, it is impossible to observe both outcomes simultaneously, which places our estimation within the domain of partial identification (PI). Pre-treatment covariates can substantially reduce estimation uncertainty by shrinking the partially identified set. Recent work has shown that covariate-assisted PI sets can be characterized through conditional optimal transport (COT) problems. However, finite-sample estimation of COT poses significant challenges, primarily because the COT functional is discontinuous under the weak topology, rendering the direct plug-in estimator inconsistent. To address this issue, existing literature relies on relaxations or indirect methods involving the estimation of non-parametric nuisance statistics. In this work, we demonstrate the continuity of the COT functional under a stronger topology induced by the adapted Wasserstein distance. Leveraging this result, we propose a direct, consistent, non-parametric estimator for COT value that avoids nuisance parameter estimation. We derive the convergence rate for our estimator and validate its effectiveness through comprehensive simulations, demonstrating its improved performance compared to existing approaches.

stat.ME↗

arXiv2025

Tightening Causal Bounds via Covariate-Aware Optimal Transport

Causal estimands can vary significantly depending on the relationship between outcomes in treatment and control groups, potentially leading to wide partial identification (PI) intervals that impede decision making. Incorporating covariates can substantially tighten these bounds, but requires determining the range of PI over probability models consistent with the joint distributions of observed covariates and outcomes in treatment and control groups. This problem is known to be equivalent to a conditional optimal transport (COT) optimization task, which is more challenging than standard optimal transport (OT) due to the additional conditioning constraints. In this work, we study a tight relaxation of COT that effectively reduces it to standard OT, leveraging its well-established computational and theoretical foundations. Our relaxation incorporates covariate information and ensures narrower PI intervals for any value of the penalty parameter, while becoming asymptotically exact as a penalty increases to infinity. This approach preserves the benefits of covariate adjustment in PI and results in a data-driven estimator for the PI set that is easy to implement using existing OT packages. We analyze the convergence rate of our estimator and demonstrate the effectiveness of our approach through extensive simulations, highlighting its practical use and superior performance compared to existing methods.

stat.ME↗

arXiv2024

Wasserstein Projection Tests: Higher-Order Asymptotics and Connections to Empirical Likelihood

Tests of moment restrictions can be constructed by projecting the empirical distribution onto the set of laws satisfying the null. Wasserstein projection (WP) performs this projection by transporting mass in the sample space, rather than only reweighting observed atoms as in empirical likelihood (EL), and therefore incorporates both the ground geometry and the local variation of the moment function. Existing WP theory provides a first-order null limit but does not quantify finite-sample calibration or distinguish tests with the same limiting local power. We derive stochastic expansions of the rescaled WP statistic under the null and under Pitman-type local alternatives, identifying its order-$n^{-1/2}$ correction with a uniform remainder of order $\widetilde{O}_p(n^{-1})$. The resulting Edgeworth theory gives an order-$\widetilde{O}(n^{-1})$ size error for the plug-in WP test and an explicit order-$n^{-1/2}$ correction to local power. For scalar moments under local location shifts, WP, EL, and Hotelling's $T^2$ have the same first-order power, whereas their second-order ranking is determined by derivative-based curvature for WP and value-based skewness for EL. Extending the expansion by one further order, we construct two Bartlett-type corrections that improve coverage accuracy to $\widetilde{O}(n^{-3/2})$. Finally, we develop a certified localized dual algorithm that controls numerical error in the test decision. A theory-guided smooth fairness experiment using a common asymptotic chi-square reference quantile finds WP power gains over the corresponding EL and $T^2$ tests in the derivative-curvature regime predicted by the comparison theory.

math.ST↗

arXiv2024

Generative Learning for Simulation of Vehicle Faults

We develop a novel generative model to simulate vehicle health and forecast faults, conditioned on practical operational considerations. The model, trained on data from the US Army's Predictive Logistics program, aims to support predictive maintenance. It forecasts faults far enough in advance to execute a maintenance intervention before a breakdown occurs. The model incorporates real-world factors that affect vehicle health. It also allows us to understand the vehicle's condition by analyzing operating data, and characterizing each vehicle into discrete states. Importantly, the model predicts the time to first fault with high accuracy. We compare its performance to other models and demonstrate its successful training.

cs.LG↗

arXiv2024

Distributionally Robust Optimization and Robust Statistics

We review distributionally robust optimization (DRO), a principled approach for constructing statistical estimators that hedge against the impact of deviations in the expected loss between the training and deployment environments. Many well-known estimators in statistics and machine learning (e.g. AdaBoost, LASSO, ridge regression, dropout training, etc.) are distributionally robust in a precise sense. We hope that by discussing the DRO interpretation of well-known estimators, statisticians who may not be too familiar with DRO may find a way to access the DRO literature through the bridge between classical results and their DRO equivalent formulation. On the other hand, the topic of robustness in statistics has a rich tradition associated with removing the impact of contamination. Thus, another objective of this paper is to clarify the difference between DRO and classical statistical robustness. As we will see, these are two fundamentally different philosophies leading to completely different types of estimators. In DRO, the statistician hedges against an environment shift that occurs after the decision is made; thus DRO estimators tend to be pessimistic in an adversarial setting, leading to a min-max type formulation. In classical robust statistics, the statistician seeks to correct contamination that occurred before a decision is made; thus robust statistical estimators tend to be optimistic leading to a min-min type formulation.

stat.ME↗

arXiv2022

Tikhonov Regularization is Optimal Transport Robust under Martingale Constraints

Distributionally robust optimization has been shown to offer a principled way to regularize learning models. In this paper, we find that Tikhonov regularization is distributionally robust in an optimal transport sense (i.e., if an adversary chooses distributions in a suitable optimal transport neighborhood of the empirical measure), provided that suitable martingale constraints are also imposed. Further, we introduce a relaxation of the martingale constraints which not only provides a unified viewpoint to a class of existing robust methods but also leads to new regularization tools. To realize these novel tools, tractable computational algorithms are proposed. As a byproduct, the strong duality theorem proved in this paper can be potentially applied to other problems of independent interest.

math.OC↗