The matrix generalized inverse Gaussian distribution: Properties and applications

Farideh Fazayeli, Arindam Banerjee

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

While the Matrix Generalized Inverse Gaussian (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 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 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 MGIG’s mode. Further, we illustrate that the the posterior distribution in latent factor models, such as probabilistic matrix factorization (PMF) [24], when marginalized over one latent factor has the 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.

Original languageEnglish (US)
Title of host publicationMachine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2016, Proceedings
EditorsJilles Giuseppe, Niels Landwehr, Giuseppe Manco, Paolo Frasconi
PublisherSpringer Verlag
Pages648-664
Number of pages17
ISBN (Print)9783319461274
DOIs
StatePublished - 2016
Event15th European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2016 - Riva del Garda, Italy
Duration: Sep 19 2016Sep 23 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9851 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other15th European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2016
CountryItaly
CityRiva del Garda
Period9/19/169/23/16

Bibliographical note

Funding Information:
The research was supported by NSF grants IIS-1447566, IIS-1447574, IIS-1422557, CCF-1451986, CNS-1314560, IIS-0953274, IIS-1029711, NASA grant NNX12AQ39A, and gifts from Adobe, IBM, and Yahoo. F.F. acknowledges the support of DDF (2015?2016) from the University of Minnesota.

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