Statistical Properties of Rectified Flow

Title

Statistical Properties of Rectified Flow

Speaker

Arun Kuchibhotla - Carnegie Mellon University

Abstract

Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these methods are scant. The rectified flow can be regarded as an approximation to optimal transport, but in contrast to other transport methods that require optimization over a function space, computing the rectified flow only requires standard statistical tools such as regression or density estimation. Because of this, one can leverage standard data analysis tools for regression and density estimation to develop empirical versions of transport maps. We study some structural properties of the rectified flow, including existence, uniqueness, and regularity, as well as the related statistical properties, such as rates of convergence and central limit theorems, for some selected estimators. To do so, we analyze separately the bounded and unbounded cases as each presents unique challenges. In both cases, we can establish convergence at faster rates than the ones for the usual nonparametric regression and density estimation. This is joint work with Gonzalo Mena and Larry Wasserman.

Bio

I am an Associate Professor in the Department of Statistics and Data Science at Carnegie Mellon University. I am also the Evergreen Junior Career Professor from 2024 to 2026. I joined CMU in September 2020. I graduated from the Wharton School of the University of Pennsylvania on May 17, 2020, with a Ph.D. in Statistics. My advisors are Lawrence D. Brown and Andreas Buja. My doctoral research concentrates on a unified framework for post-selection inference. My research interests include post-selection inference, large sample theory, uniformly valid inference, robust statistics, semi-parametric statistics, non-parametric statistics, concentration inequalities, high-dimensional CLT, and dependent data.

When

Thursday, December 4th, 15:00

Where

Room 322, UniGe DIBRIS/DIMA, Via Dodecaneso 35