Related papers: A Wasserstein Minimum Velocity Approach to Learnin…

Wasserstein distributionally robust optimization (WDRO) strengthens statistical learning under model uncertainty by minimizing the local worst-case risk within a prescribed ambiguity set. Although WDRO has been extensively studied in…

Gradient-based dimension reduction decreases the cost of Bayesian inference and probabilistic modeling by identifying maximally informative (and informed) low-dimensional projections of the data and parameters, allowing high-dimensional…

This paper studies minimax optimization problems defined over infinite-dimensional function classes of overparameterized two-layer neural networks. In particular, we consider the minimax optimization problem stemming from estimating linear…

The success of autoregressive models largely depends on the effectiveness of vector quantization, a technique that discretizes continuous features by mapping them to the nearest code vectors within a learnable codebook. Two critical issues…

We extend Stein's celebrated Wasserstein bound for normal approximation via exchangeable pairs to the multi-dimensional setting. As an intermediate step, we exploit the symmetry of exchangeable pairs to obtain an error bound for smooth test…

Learning conditional densities and identifying factors that influence the entire distribution are vital tasks in data-driven applications. Conventional approaches work mostly with summary statistics, and are hence inadequate for a…

Quantification of uncertainty is one of the most promising approaches to establish safe machine learning. Despite its importance, it is far from being generally solved, especially for neural networks. One of the most commonly used…

Transductive few-shot learning algorithms have showed substantially superior performance over their inductive counterparts by leveraging the unlabeled queries. However, the vast majority of such methods are evaluated on perfectly…

We propose to align distributional data from the perspective of Wasserstein means. We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the…

A major focus in designing methods for learning distributions defined on manifolds is to alleviate the need to implicitly learn the manifold so that learning can concentrate on the data distribution within the manifold. However,…

The performance of machine learning (ML) models critically depends on the quality and representativeness of the training data. In applications with multiple heterogeneous data generating sources, standard ML methods often learn spurious…

One approach to matching texts from asymmetrical domains is projecting the input sequences into a common semantic space as feature vectors upon which the matching function can be readily defined and learned. In real-world matching…

We consider a general task called partial Wasserstein covering with the goal of providing information on what patterns are not being taken into account in a dataset (e.g., dataset used during development) compared with another dataset(e.g.,…

This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental…

Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…

Distribution matching (DM) is a versatile domain-invariant representation learning technique that has been applied to tasks such as fair classification, domain adaptation, and domain translation. Non-parametric DM methods struggle with…

Classifying large-scale image data into object categories is an important problem that has received increasing research attention. Given the huge amount of data, non-parametric approaches such as nearest neighbor classifiers have shown…

Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…

We propose a novel word embedding pre-training approach that exploits writing errors in learners' scripts. We compare our method to previous models that tune the embeddings based on script scores and the discrimination between correct and…

Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear…