Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Spectral Approach to Gradient Estimation for Implicit Distributions   Recently there have been increasing interests in learning and inference with
implicit distributions (i.e., distributions without tractable densities). To
this end, we develop a gradient estimator for implicit distributions based on
Stein's identity and a spectral decomposition of kernel operators, where the
eigenfunctions are approximated by the Nystr\"om method. Unlike the previous
works that only provide estimates at the sample points, our approach directly
estimates the gradient function, thus allows for a simple and principled
out-of-sample extension. We provide theoretical results on the error bound of
the estimator and discuss the bias-variance tradeoff in practice. The
effectiveness of our method is demonstrated by applications to gradient-free
Hamiltonian Monte Carlo and variational inference with implicit distributions.
Finally, we discuss the intuition behind the estimator by drawing connections
between the Nystr\"om method and kernel PCA, which indicates that the estimator
can automatically adapt to the geometry of the underlying distribution.

31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int