相关论文: Ambiguity set and learning via Bregman and Wassers…

Information divergence that measures the difference between two nonnegative matrices or tensors has found its use in a variety of machine learning problems. Examples are Nonnegative Matrix/Tensor Factorization, Stochastic Neighbor…

Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost…

We present a provably safe sampling-based motion planning algorithm for robotic systems affected by random disturbances of unknown distribution. We consider systems with linear or linearizable dynamics evolving in workspace with…

Precise control under uncertainty requires a good understanding and characterization of the noise affecting the system. This paper studies the problem of steering state distributions of dynamical systems subject to partially known…

This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent…

Structuring ambiguity sets in Wasserstein-based distributionally robust optimization (DRO) can improve their statistical properties when the uncertainty consists of multiple independent components. The aim of this paper is to solve…

The Wasserstein distance, rooted in optimal transport (OT) theory, is a popular discrepancy measure between probability distributions with various applications to statistics and machine learning. Despite their rich structure and…

Classical linear metric learning methods have recently been extended along two distinct lines: deep metric learning methods for learning embeddings of the data using neural networks, and Bregman divergence learning approaches for extending…

Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant…

This paper addresses a new active learning strategy for regression problems. The presented Wasserstein active regression model is based on the principles of distribution-matching to measure the representativeness of the labeled dataset. The…

In this work, we study how to ensure probabilistic safety for nonlinear systems under distributional ambiguity. Our approach builds on a backup-based safety filtering framework that switches between a high-performance nominal policy and a…

We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence. We show that Sinkhorn-based algorithms can approximate the optimal cost…

The discrete distribution is often used to describe complex instances in machine learning, such as images, sequences, and documents. Traditionally, clustering of discrete distributions (D2C) has been approached using Wasserstein barycenter…

Unsupervised learning of disentangled representations involves uncovering of different factors of variations that contribute to the data generation process. Total correlation penalization has been a key component in recent methods towards…

We propose a new unsupervised anomaly detection method based on the sliced-Wasserstein distance for training data selection in machine learning approaches. Our filtering technique is interesting for decision-making pipelines deploying…

A loss function measures the discrepancy between the true values and their estimated fits, for a given instance of data. In classification problems, a loss function is said to be proper if a minimizer of the expected loss is the true…

Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…

This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…

In this paper, we propose a novel robust stochastic optimization approach with a distinctive consideration for rare events, in which divergence measures are used to bound the event-wise ambiguity sets. This is done by using the Poisson…

Building on a recent framework for distributionally robust optimization, we consider estimation of the inverse covariance matrix for multivariate data. We provide a novel notion of a Wasserstein ambiguity set specifically tailored to this…