 Award ID(s):
 1751636
 Publication Date:
 NSFPAR ID:
 10232664
 Journal Name:
 Proceedings of the AAAI Conference on Artificial Intelligence
 Volume:
 35
 Issue:
 118
 ISSN:
 23743468
 Sponsoring Org:
 National Science Foundation
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Triangular flows, also known as KnötheRosenblatt measure couplings, comprise an important building block of normalizing flow models for generative modeling and density estimation, including popular autoregressive flows such as realvalued nonvolume 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 KullbackLeibler divergence statistical estimator of the KnötheRosenblatt 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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