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This content will become publicly available on January 1, 2023

Title: Triangular Flows for Generative Modeling: Statistical Consistency, Smoothness Classes, and Fast Rates
Triangular flows, also known as Knöthe-Rosenblatt measure couplings, comprise an important building block of normalizing flow models for generative modeling and density estimation, including popular autoregressive flows such as real-valued non-volume preserving transformation models (Real NVP). We present statistical guarantees and sample complexity bounds for triangular flow statistical models. In particular, we establish the statistical consistency and the finite sample convergence rates of the minimum Kullback-Leibler divergence statistical estimator of the Knöthe-Rosenblatt measure coupling using tools from empirical process theory. Our results highlight the anisotropic geometry of function classes at play in triangular flows, shed light on optimal coordinate ordering, and lead to statistical guarantees for Jacobian flows. We conduct numerical experiments to illustrate the practical implications of our theoretical findings.
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Award ID(s):
2134012 2023166 2133244
Publication Date:
Journal Name:
Proceedings of Machine Learning Research
Page Range or eLocation-ID:
Sponsoring Org:
National Science Foundation
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