Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalities

arXiv:2403.02004v1 Announce Type: new
Abstract: We prove non-asymptotic error bounds for particle gradient descent (PGD)~(Kuntz et al., 2023), a recently introduced algorithm for maximum likelihood estimation of large latent variable models obtained by discretizing a gradient flow of the free energy. We begin by showing that, for models satisfying a condition generalizing both the log-Sobolev and the Polyak--{\L}ojasiewicz inequalities (LSI and P{\L}I, respectively), the flow converges exponentially fast to the set of minimizers of the free energy. We achieve this …

abstract algorithm arxiv cs.lg energy error extensions flow free gradient likelihood math.fa math.oc maximum likelihood estimation particle prove stat.co stat.ml type