Paper Info
Title
The Matrix Generalized Inverse Gaussian Distribution: Properties and Applications.
Abstract
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 equationï¾ź[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 approachesï¾ź[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 PMFï¾ź[24], 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.
Year
DOI
Venue
2016
10.1007/978-3-319-46128-1_41
ECML/PKDD
Field
DocType
Citations 
Monte Carlo method,Importance sampling,Mathematical optimization,Markov chain Monte Carlo,Matrix (mathematics),Generalized inverse,Generalized inverse Gaussian distribution,Gaussian,Algebraic Riccati equation,Mathematics
Conference
0
PageRank 
References 
Authors
0.34
9
2
Name
Order
Citations
PageRank
Farideh Fazayeli1966.81
Arindam Banerjee2313.77