Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-Dimensional Non-Parametric Density Estimation in Mixed Smooth
  Sobolev Spaces   Density estimation plays a key role in many tasks in machine learning,
statistical inference, and visualization. The main bottleneck in
high-dimensional density estimation is the prohibitive computational cost and
the slow convergence rate. In this paper, we propose novel estimators for
high-dimensional non-parametric density estimation called the adaptive
hyperbolic cross density estimators, which enjoys nice convergence properties
in the mixed smooth Sobolev spaces. As modifications of the usual Sobolev
spaces, the mixed smooth Sobolev spaces are more suitable for describing
high-dimensional density functions in some applications. We prove that, unlike
other existing approaches, the proposed estimator does not suffer the curse of
dimensionality under Integral Probability Metric, including H\"older Integral
Probability Metric, where Total Variation Metric and Wasserstein Distance are
special cases. Applications of the proposed estimators to generative
adversarial networks (GANs) and goodness of fit test for high-dimensional data
are discussed to illustrate the proposed estimator's good performance in
high-dimensional problems. Numerical experiments are conducted and illustrate
the efficiency of our proposed method.

17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg