Related papers: Wasserstein Least Squares: A Canonical Regression …
The conventional sliced Wasserstein is defined between two probability measures that have realizations as vectors. When comparing two probability measures over images, practitioners first need to vectorize images and then project them to…
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…
We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where…
Wasserstein geometry and information geometry are two important structures to be introduced in a manifold of probability distributions. Wasserstein geometry is defined by using the transportation cost between two distributions, so it…
Standard stochastic control methods assume that the probability distribution of uncertain variables is available. Unfortunately, in practice, obtaining accurate distribution information is a challenging task. To resolve this issue, we…
Fr\'echet regression, or conditional Barycenters, is a flexible framework for modeling relationships between covariates (usually Euclidean) and response variables on general metric spaces, e.g., probability distributions or positive…
We consider a resampling scheme for parameters estimates in nonlinear regression models. We provide an estimation procedure which recycles, via random weighting, the relevant parameters estimates to construct consistent estimates of the…
We develop a kernel projected Wasserstein distance for the two-sample test, an essential building block in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. This method…
Using only retrospective data, we study the problem of predicting treatment effects for the same treatment/policy implemented in a different location or time period. We propose a distributionally robust estimator that minimizes the…
We develop a framework of canonical correlation analysis for distribution-valued functional data within the geometry of Wasserstein spaces. Specifically, we formulate an intrinsic concept of correlation between random distributions, propose…
The optimal transport barycenter (a.k.a. Wasserstein barycenter) is a fundamental notion of averaging that extends from the Euclidean space to the Wasserstein space of probability distributions. Computation of the unregularized barycenter…
Recent work has leveraged the popular distributionally robust optimization paradigm to combat overfitting in classical logistic regression. While the resulting classification scheme displays a promising performance in numerical experiments,…
We develop a general theory to address a consensus-based combination of estimations in a parallelized or distributed estimation setting. Taking into account the possibility of very discrepant estimations, instead of a full consensus we…
We study the multivariate deconvolution problem of recovering the distribution of a signal from independent and identically distributed observations additively contaminated with random errors (noise) from a known distribution. For errors…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
Problem definition: A key challenge in supervised learning is data scarcity, which can cause prediction models to overfit to the training data and perform poorly out of sample. A contemporary approach to combat overfitting is offered by…
The paper considers the distribution of a general linear combination of central and non-central chi-square random variables by exploring the branch cut regions that appear in the standard Laplace inversion process. Due to the original…
Having a regression model, we are interested in finding two-sided intervals that are guaranteed to contain at least a desired proportion of the conditional distribution of the response variable given a specific combination of predictors. We…
Wasserstein distributionally robust control (WDRC) is an effective method for addressing inaccurate distribution information about disturbances in stochastic systems. It provides various salient features, such as an out-of-sample…
The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…