Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Matrix Generalized Inverse Gaussian Distribution: Properties and
  Applications   While the Matrix Generalized Inverse Gaussian ($\mathcal{MGIG}$) distribution
arises naturally in some settings as a distribution over symmetric positive
semi-definite matrices, certain key properties of the distribution and
effective ways of sampling from the distribution have not been carefully
studied. In this paper, we show that the $\mathcal{MGIG}$ is unimodal, and the
mode can be obtained by solving an Algebraic Riccati Equation (ARE) equation
[7]. Based on the property, we propose an importance sampling method for the
$\mathcal{MGIG}$ where the mode of the proposal distribution matches that of
the target. The proposed sampling method is more efficient than existing
approaches [32, 33], which use proposal distributions that may have the mode
far from the $\mathcal{MGIG}$'s mode. Further, we illustrate that the the
posterior distribution in latent factor models, such as probabilistic matrix
factorization (PMF) [25], when marginalized over one latent factor has the
$\mathcal{MGIG}$ distribution. The characterization leads to a novel Collapsed
Monte Carlo (CMC) inference algorithm for such latent factor models. We
illustrate that CMC has a lower log loss or perplexity than MCMC, and needs
fewer samples.

21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
9
The categories of this paper are: nlin