Stat Colloquium: Dr. Ray Bai

Despite their appeal, DGMs often struggle to learn heavy-tailed distributions. In the second project, we analyze the fundamental nature of this limitation through the lens of functional inequalities. We show that under the widely used Gaussian source distribution, the transport map must necessarily have increasingly large norm as the target distribution's moments become larger. These results are then extended to general log-concave source distributions. Notably, our results are intrinsic to the underlying transport problem and are independent of specific architectures, parameterizations, or training schemes.  This has several practical implications for the design and analysis of DGMs.