On the representation and learning of monotone triangular transport maps

arXiv:2009.10303v3 Announce Type: replace-cross
Abstract: Transportation of measure provides a versatile approach for modeling complex probability distributions, with applications in density estimation, Bayesian inference, generative modeling, and beyond. Monotone triangular transport maps$\unicode{x2014}$approximations of the Knothe$\unicode{x2013}$Rosenblatt (KR) rearrangement$\unicode{x2014}$are a canonical choice for these tasks. Yet the representation and parameterization of such maps have a significant impact on their generality and expressiveness, and on properties of the optimization problem that arises in learning a map from data (e.g., via maximum likelihood estimation). …

abstract applications arxiv bayesian bayesian inference beyond canonical cs.lg generative generative modeling inference maps math.fa modeling probability representation stat.co stat.me stat.ml tasks transport transportation type unicode