An Approximation Theory Framework for Measure-Transport Sampling Algorithms

Understand

This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling.

• A primary motivating application for such algorithms is sampling -- a central task in statistical inference and generative modeling.
• We provide a priori error estimates in the continuum limit, i.e., when the measures (or their densities) are given, but when the transport map is discretized or approximated using a finite-dimensional function space.
• Our analysis relies on the regularity theory of transport maps and on classical approximation theory for high-dimensional functions.