Creating Transport Maps with MParT.jl

Measure Transport, "moving" from one measure to another, has been gaining momentum to perform generative sampling, conditional density estimation, and other statistical methods on a computer. However, transport software is primarily bespoke, is not portable, and can be slow. The Monotone Parameterization Toolkit (MParT) package provides a fast, tested base in C++ to train and use complicated maps for transport easily, and we highlight the Julia bindings for the package in this talk.

The Monotone Parameterization Toolkit (MParT) is a software package written in C++ with bindings in Python, Matlab, and Julia to parameterize and train a subclass of functions that perform measure transport, called Monotone Transport Maps. The tooling required includes adaptive quadrature, orthogonal polynomials, and more, which is why there has yet to be a comprehensive package to perform monotone transport. Built around Kokkos, MParT allows users to effortlessly work with these maps, and do the vast majority of calculations in parallel with ongoing efforts to allow GPU calculations. This talk is intended to be a small introduction of what MParT has to offer with a few interesting examples of training and using maps for different simple statistical modeling problems.