Closed-form marginal likelihood in Gamma-Poisson factorization

01/05/2018
by   Louis Filstroff, et al.
0

We present novel understandings of the Gamma-Poisson (GaP) model, a probabilistic matrix factorization model for count data. We show that GaP can be rewritten free of the score/activation matrix. This gives us new insights about the estimation of the topic/dictionary matrix by maximum marginal likelihood estimation. In particular, this explains the robustness of this estimator to over-specified values of the factorization rank and in particular its ability to automatically prune spurious dictionary columns, as empirically observed in previous work. The marginalization of the activation matrix leads in turn to a new Monte-Carlo Expectation-Maximization algorithm with favorable properties.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/30/2015

Nonparametric Bayesian Factor Analysis for Dynamic Count Matrices

A gamma process dynamic Poisson factor analysis model is proposed to fac...
research
01/05/2018

Negative Binomial Matrix Factorization for Recommender Systems

We introduce negative binomial matrix factorization (NBMF), a matrix fac...
research
06/23/2020

A Comparative Study of Temporal Non-Negative Matrix Factorization with Gamma Markov Chains

Non-negative matrix factorization (NMF) has become a well-established cl...
research
02/18/2020

Observational nonidentifiability, generalized likelihood and free energy

We study the parameter estimation problem in mixture models with observa...
research
05/29/2019

Noisy and Incomplete Boolean Matrix Factorizationvia Expectation Maximization

Probabilistic approach to Boolean matrix factorization can provide solut...
research
04/13/2016

Hierarchical Compound Poisson Factorization

Non-negative matrix factorization models based on a hierarchical Gamma-P...
research
02/23/2019

A unified perspective on modified Poisson likelihoods for limited Monte Carlo data

Counting experiments often rely on Monte Carlo simulations for predictio...

Please sign up or login with your details

Forgot password? Click here to reset