Sample Out-Of-Sample Inference Based on Wasserstein Distance

Abstract

We present a novel inference approach that we call Sample Out-of-Sample (or SOS) inference. The approach can be used widely, ranging from semi-supervised learning to stress testing, and it is fundamental in the application of data-driven Distributionally Robust Optimization (DRO). Our method enables measuring the impact of plausible out-of-sample scenarios in a given performance measure of interest, such as a financial loss. The methodology is inspired by Empirical Likelihood (EL), but we optimize the empirical Wasserstein distance (instead of the empirical likelihood) induced by observations. From a methodological standpoint, our analysis of the asymptotic behavior of the induced Wasserstein-distance profile function shows dramatic qualitative differences relative to EL. For instance, in contrast to EL, which typically yields chi-squared weak convergence limits, our asymptotic distributions are often not chi-squared. Also, the rates of convergence that we obtain have some dependence on the dimension in a non-trivial way but remain controlled as the dimension increases.

References in corpus (12)

• Generalizing to Unseen Domains via Adversarial Data Augmentation
• Robust Wasserstein Profile Inference and Applications to Machine Learning
• Extending the scope of empirical likelihood
• Does Distributionally Robust Supervised Learning Give Robust Classifiers?
• Distributionally Robust Stochastic Optimization with Wasserstein Distance
• Data-Driven Chance Constrained Programs over Wasserstein Balls
• Robust Hypothesis Testing Using Wasserstein Uncertainty Sets
• Learning Models with Uniform Performance via Distributionally Robust Optimization
• Semi-supervised Learning based on Distributionally Robust Optimization
• Data-driven Optimal Cost Selection for Distributionally Robust Optimization
• Doubly Robust Data-Driven Distributionally Robust Optimization
• A Distributionally Robust Boosting Algorithm

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• Combating Conservativeness in Data-Driven Optimization under Uncertainty: A Solution Path Approach
• Optimization-based Quantification of Simulation Input Uncertainty via Empirical Likelihood
• An Uncertainty Quantification Method for Inexact Simulation Models
• Distributionally Robust Martingale Optimal Transport
• Higher-Order Expansion and Bartlett Correctability of Distributionally Robust Optimization
• Orthounimodal Distributionally Robust Optimization: Representation, Computation and Multivariate Extreme Event Applications
• Human Imperceptible Attacks and Applications to Improve Fairness