Bayesian learning with Wasserstein barycenters
We introduce and study a novel model-selection strategy for Bayesian learning based on optimal transport (OT): the Wasserstein population barycenter of the posterior distribution over models. We motivate the introduction of the Bayesian Wasserstein barycenter (BWB) in both the parametric and parameter-free Bayesian model-selection frameworks with illustrative examples. In addition to the results in [1], we will explore ways of implementing BWB based on [2] for practical machine learning problems where the generative models are constrained to be Gaussian mixtures. If time allows, we will also revise the use of weak OT barycenters for clustering of distributions based on [3].
[1] J. Backhoff-Veraguas, J. Fontbona, G. Rios, F. Tobar (2022), Bayesian learning with Wasserstein barycenters, ESAIM: Probability and Statistics, vol. 26, p. 436-472
[2] J. Delon and A. Desolneux (2020), A Wasserstein-type distance in the space of Gaussian Mixture Models, SIAM Journal on Imaging Sciences, vol. 13(2), p. 936-970
[3] E. Cazelles, F. Tobar, J. Fontbona (2021), A novel notion of barycenter for probability distributions based on optimal weak mass transport, Advances on neural information processing systems