Year: 2018
Type: preprint
Abstract: We introduce and study a novel model-selection strategy for Bayesian learning, based on optimal transport, along with its associated predictive posterior law: the Wasserstein population barycenter of the posterior law over models. We first show how this estimator, termed Bayesian Wasserstein barycenter (BWB), arises naturally in a general, parameter-free Bayesian model-selection framework, when the considered Bayesian risk is the Wasserstein distance. Examples are given, illustrating how the BWB extends some classic parametric and non-parametric selection strategies. Furthermore, we also provide explicit conditions granting the existence and statistical consistency of the BWB, and discuss some of its general and specific properties, providing insights into its advantages compared to usual choices, such as the model average estimator. Finally, we illustrate how this estimator can be computed using the stochastic gradient descent (SGD) algorithm in Wasserstein space introduced in a companion paper arXiv:2201.04232v2 [math.OC], and provide a numerical example for experimental validation of the proposed method.
Source: arXiv (Cornell University)
Authors: Backhoff-Veraguas, Julio, Fontbona, Joaquin, Rios, Gonzalo, Tobar, Felipe
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: ADVANCES ON GENERATIVE MODELS FOR STATISTICAL MACHINE LEARNING THEORY AND PRACTICE, PROPAGATION OF CHAOS AND LONGTIME BEHAVIOR FOR SOME MEAN FIELD INTERACTING PARTICLE SYSTEMS FROM MATHEMATICAL PHYSICS AND MATHEMATICAL BIOLOGY, ADVANCED CENTER FOR ELECTRICAL AND ELECTRONIC ENGINEERING, CENTER FOR MATHEMATICAL MODELING (CMM), CENTRO DE MODELAMIENTO MATEMATICO
OpenAlex ID: W4290737015