相关论文: Transfer Operators from Batches of Unpaired Points…

We propose a new concept for the regularization and discretization of transfer and Koopman operators in dynamical systems. Our approach is based on the entropically regularized optimal transport between two probability measures. In…

We study inference in stochastic block models (SBMs) through the lens of optimal transport (OT). We first establish that maximum likelihood variational inference (MLVI) can be interpreted as a semi-relaxed Gromov-Wasserstein (srGW)…

For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…

This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek…

This paper proposes a new method of bandwidth selection in kernel estimation of density and distribution functions motivated by the connection between maximisation of the entropy of probability integral transforms and maximum likelihood in…

Learning conditional distributions $\pi^*(\cdot|x)$ is a central problem in machine learning, which is typically approached via supervised methods with paired data $(x,y) \sim \pi^*$. However, acquiring paired data samples is often…

Empirical data can often be considered as samples from a set of probability distributions. Kernel methods have emerged as a natural approach for learning to classify these distributions. Although numerous kernels between distributions have…

Transporting findings from a study population to a target population is central to evidence-based decision-making in real-world settings. Most existing methods require individual-level data from both populations to account for covariate…

We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…

Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic…

We study a family of discrete-time random-walk models. The starting point is a fixed generalized transfer operator $R$ subject to a set of axioms, and a given endomorphism in a compact Hausdorff space $X$. Our setup includes a host of…

We generalize the well-known mixtures of Gaussians approach to density estimation and the accompanying Expectation--Maximization technique for finding the maximum likelihood parameters of the mixture to the case where each data point…

It is known that non-commuting observables in quantum mechanics do not have joint probability. This statement refers to the precise (additive) probability model. I show that the joint distribution of any non-commuting pair of variables can…

Uncertainty is ubiquitous in real-world data, and the assumptions underlying classical linear regression models are often violated in practice. Inspired by the theory of sublinear expectation, we consider a linear regression model where the…

Dynamical systems can be analyzed via their Frobenius-Perron transfer operator and its estimation from data is an active field of research. Recently entropic transfer operators have been introduced to estimate the operator of deterministic…

We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…

Recently, some works have suggested methods to combine variational probabilistic inference with Monte Carlo sampling. One promising approach is via local optimal transport. In this approach, a gradient steepest descent method based on local…

Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often uninterpretable. In this article, we offer a novel alternative by constructing an exponentially tilted…

We develop a new methodology for model-based clustering. Optimizing the log-likelihood provides a principled statistical framework for clustering, with solutions found via the EM algorithm. However, because the log-likelihood is nonconvex,…

Data transformation, e.g. feature transformation and selection, is an integral part of any machine learning procedure. In this paper we introduce an information-theoretic model and tools to assess the quality of data transformations in…