Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 estimate the
target distribution consistently due to the singularity. We prove that a novel
and effective solution exists by perturbing the data with an instance noise
which leads to consistent estimation of the underlying distribution with
desirable convergence rates. We also characterize the class of distributions
that can be efficiently estimated via deep generative models. This class is
sufficiently general to contain various structured distributions such as
product distributions, classically smooth distributions and distributions
supported on a low-dimensional manifold. Our analysis provides some insights on
how deep generative models can avoid the curse of dimensionality for
nonparametric distribution estimation. We conduct thorough simulation study and
real data analysis to empirically demonstrate that the proposed data
perturbation technique improves the estimation performance significantly.

10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
3
The categories of this paper are: physics
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin