Normalizing flows provide a general mechanism for defining expressive probability
distributions, only requiring the specification of a (usually simple) base distribution and a …

Normalizing Flows are generative models which produce tractable distributions where both
sampling and density evaluation can be efficient and exact. The goal of this survey article is …

Questions of 'how best to acquire data'are essential to modelling and prediction in the
natural and social sciences, engineering applications, and beyond. Optimal experimental …

At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …

Includes material for a standard graduate class, advanced material not covered by the
standard course but necessary in order to read research literature in the area, and extensive …

Invertible neural networks based on coupling flows (CF-INNs) have various machine
learning applications such as image synthesis and representation learning. However, their …

Triangular map is a recent construct in probability theory that allows one to transform any
source probability density function to any target density function. Based on triangular maps …

This book provides the reader with the principal concepts and results related to differential
properties of measures on infinite dimensional spaces. In the finite dimensional case such …

We investigate the low-dimensional structure of deterministic transformations between
random variables, ie, transport maps between probability measures. In the context of …

We consider filtering in high-dimensional non-Gaussian state-space models with intractable
transition kernels, nonlinear and possibly chaotic dynamics, and sparse observations in …