Related papers: Measure Transport with Kernel Stein Discrepancy
In this paper we investigate systems previously identified to exhibit transit timing variations (TTVs) in Kepler data, with the goal of predicting the expected improvements to the mass and eccentricity constraints that will arise from…
We apply two variations of the principle of Minimum Cross Entropy (the Kullback information measure) to fit parameterized probability density models to observed data densities. For an array beamforming problem with P incident narrowband…
Kullback-Leibler divergence (KL) regularization is widely used in reinforcement learning, but it becomes infinite under support mismatch and can degenerate in low-noise limits. Utilizing a unified information-geometric framework, we…
In this paper, we discuss a property of the Kullback--Leibler divergence measured between two models of the family of the location-scale distributions. We show that, if model $M_1$ and model $M_2$ are represented by location-scale…
The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback-Leibler distance to measure the performance of filtering algorithms in…
Finding the proper entropy-like Lyapunov functional associated with the inelastic Boltzmann equation for an isolated freely cooling granular gas is a still unsolved challenge. The original $H$-theorem hypotheses do not fit here and the…
In this study, we establish a basis for selecting similarity measures when applying machine learning techniques to solve materials science problems. This selection is considered with an emphasis on the distinctiveness between materials that…
We develop connections between Stein's approximation method, logarithmic Sobolev and transport inequalities by introducing a new class of functional inequalities involving the relative entropy, the Stein kernel, the relative Fisher…
Positivity of the prior probability of Kullback-Leibler neighborhood around the true density, commonly known as the Kullback-Leibler property, plays a fundamental role in posterior consistency. A popular prior for Bayesian estimation is…
This is the first part of a general description in terms of mass transport for time-evolving interacting particles systems, at a mesoscopic level. Beyond kinetic theory, our framework naturally applies in biology, computer vision, and…
We study Benamou's domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove…
Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the last decade, two relaxations of optimal transport have been…
In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
Stein discrepancies (SDs) monitor convergence and non-convergence in approximate inference when exact integration and sampling are intractable. However, the computation of a Stein discrepancy can be prohibitive if the Stein operator - often…
We derive a deterministic, non-asymptotic upper bound on the Kullback-Leibler (KL) divergence of the flow-matching distribution approximation. In particular, if the $L_2$ flow-matching loss is bounded by $\epsilon^2 > 0$, then the KL…
We develop a discrete optimal transport framework for analyzing simulated annealing algorithms on finite state spaces. Building on the discrete Wasserstein metric introduced by Maas (J. Funct. Anal., 2011), we define a generalized discrete…
In this paper we prove the optimality of an aggregation procedure. We prove lower bounds for aggregation of model selection type of $M$ density estimators for the Kullback-Leiber divergence (KL), the Hellinger's distance and the…
We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…