Diffeomorphic Measure Matching with Kernels for Generative Modeling

This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs), inspired by ideas from diffeomorphic matching and image registration. A theoretical analysis of the proposed method is presented, giving a priori error bounds in terms of the complexity of the model, the number of samples in the training set, and model misspecification. An extensive suite of numerical experiments further highlights …

analysis article cs.lg differential divergence error framework general generative generative modeling giving ideas image kernel math.ds modeling ordinary probability registration sampling spaces stat.co stat.ml transport