A0272
Title: Deep generative models for nonparametric estimation of singular distributions
Authors: Minwoo Chae - Pohang University of Science and Technology (Korea, South) [presenting]
Abstract: While deep generative models are popularly used to model high-dimensional data, theoretical understanding of it is largely unexplored. We investigate the statistical properties of deep generative models from a nonparametric distribution estimation viewpoint. In the considered model, data are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure is challenging due to its singularity. In particular, a likelihood approach can fail to estimate the target distribution consistently. We obtain convergence rates with respect to the Wasserstein metric for two methods: a sieve MLE based on the perturbed data and a GAN type estimator. Our analysis gives some insights into i) how deep generative models can avoid the curse of dimensionality, ii) how likelihood approaches work for singular distribution estimation, and iii) why GAN performs better than likelihood approaches.
