Related papers: Wasserstein Variational Inference
Wasserstein distributionally robust optimization (WDRO) attempts to learn a model that minimizes the local worst-case risk in the vicinity of the empirical data distribution defined by Wasserstein ball. While WDRO has received attention as…
Optimal transport is widely used to learn distributions, enforce distributional constraints, and model uncertainty. In applications, transport losses are often computed from samples through tractable representations, such as one-dimensional…
Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…
Composite quantile regression has been used to obtain robust estimators of regression coefficients in linear models with good statistical efficiency. By revealing an intrinsic link between the composite quantile regression loss function and…
Bayesian inference plays an important role in advancing machine learning, but faces computational challenges when applied to complex models such as deep neural networks. Variational inference circumvents these challenges by formulating…
Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or…
Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al.,…
We introduce a novel optimal transport framework for probabilistic circuits (PCs). While it has been shown recently that divergences between distributions represented as certain classes of PCs can be computed tractably, to the best of our…
We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent variable models of the data distribution based on the primal and the dual formulations of the optimal transport (OT) problem. We utilize the primal…
We derive first-order (in the stepsize) bounds on the bias in Wasserstein distances of the invariant measure of stochastic gradient kinetic Langevin dynamics with minimal assumptions on the stochastic gradient noise. These bounds sharpen…
Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport. They are difficult to compute in practice, however, leading previous work to restrict their…
Anomaly detection (AD) has been an active research area in various domains. Yet, the increasing data scale, complexity, and dimension turn the traditional methods into challenging. Recently, the deep generative model, such as the…
This paper presents a new approach to the classical problem of quantifying posterior contraction rates (PCRs) in Bayesian statistics. Our approach relies on Wasserstein distance, and it leads to two main contributions which improve on the…
Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This…
In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances…
Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family, minimizing a loss that is typically the (reverse) Kullback-Leibler (KL)…
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
Wasserstein distance, which measures the discrepancy between distributions, shows efficacy in various types of natural language processing (NLP) and computer vision (CV) applications. One of the challenges in estimating Wasserstein distance…
Self-supervised learning is one of the most promising approaches to acquiring knowledge from limited labeled data. Despite the substantial advancements made in recent years, self-supervised models have posed a challenge to practitioners, as…
We introduce weak barycenters of a family of probability distributions, based on the recently developed notion of optimal weak transport of mass by Gozlanet al. (2017) and Backhoff-Veraguas et al. (2020). We provide a theoretical analysis…