Conditional density estimation through optimal transport

Esteban Tabak
Courant Institute, New York University

Conditional probability estimation and simulation provides data-based answers to all kinds of critical questions, such as the response of specific patients to different medical treatments, the effect of political measures on the economy, and weather and climate forecasts. In the complex systems behind these examples, the outcome of a process depends on many and diverse factors and is probabilistic in nature, due in part to our ignorance of other relevant factors and to the chaotic nature of the underlying dynamics.
This talk will describe a general procedure for the estimation and simulation of conditional probabilities based on two complementary ideas: the removal of the effect of covariates through a data-based, generalized optimal transport barycenter problem, and the reduction of complexity through a low-rank tensor factorization/separation of variables procedure extended to variables of any type.