A Likelihood Approach to Nonparametric Estimation of a Singular Distribution Using Deep Generative Models

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to …

ambient data deep generative models distribution generative generative models likelihood low manifold singularity space statistical