Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A particle-based variational approach to Bayesian Non-negative Matrix
  Factorization   Bayesian Non-negative Matrix Factorization (NMF) is a promising approach for
understanding uncertainty and structure in matrix data. However, a large volume
of applied work optimizes traditional non-Bayesian NMF objectives that fail to
provide a principled understanding of the non-identifiability inherent in NMF--
an issue ideally addressed by a Bayesian approach. Despite their suitability,
current Bayesian NMF approaches have failed to gain popularity in an applied
setting; they sacrifice flexibility in modeling for tractable computation, tend
to get stuck in local modes, and require many thousands of samples for
meaningful uncertainty estimates. We address these issues through a
particle-based variational approach to Bayesian NMF that only requires the
joint likelihood to be differentiable for tractability, uses a novel
initialization technique to identify multiple modes in the posterior, and
allows domain experts to inspect a `small' set of factorizations that
faithfully represent the posterior. We introduce and employ a class of
likelihood and prior distributions for NMF that formulate a Bayesian model
using popular non-Bayesian NMF objectives. On several real datasets, we obtain
better particle approximations to the Bayesian NMF posterior in less time than
baselines and demonstrate the significant role that multimodality plays in
NMF-related tasks.

26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
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
3
The categories of this paper are: physics