Nonparametric Bayesian Factor Analysis for Dynamic Count Matrices

Abstract

A gamma process dynamic Poisson factor analysis model is proposed to factorize a dynamic count matrix, whose columns are sequentially observed count vectors. The model builds a novel Markov chain that sends the latent gamma random variables at time $(t-1)$ as the shape parameters of those at time $t$, which are linked to observed or latent counts under the Poisson likelihood. The significant challenge of inferring the gamma shape parameters is fully addressed, using unique data augmentation and marginalization techniques for the negative binomial distribution. The same nonparametric Bayesian model also applies to the factorization of a dynamic binary matrix, via a Bernoulli-Poisson link that connects a binary observation to a latent count, with closed-form conditional posteriors for the latent counts and efficient computation for sparse observations. We apply the model to text and music analysis, with state-of-the-art results.

Appeared in Artificial Intelligence and Statistics (AISTATS), May 2015. The ArXiv version fixes a typo in (8), the equation right above Section 3.2 in Page 4 of http://www.jmlr.org/proceedings/papers/v38/acharya15.pdf

References in corpus (5)

• Modeling Temporal Dependencies in High-Dimensional Sequences: Application to Polyphonic Music Generation and Transcription
• Beta-Negative Binomial Process and Poisson Factor Analysis
• Stochastic expansions using continuous dictionaries: Lévy adaptive regression kernels
• Effective Bayesian Modeling of Groups of Related Count Time Series
• Augment-and-Conquer Negative Binomial Processes

Cited by in corpus (13)

• Dynamic Poisson Factorization
• Variational Temporal Deep Generative Model for Radar HRRP Target Recognition
• Deep Temporal Sigmoid Belief Networks for Sequence Modeling
• Recommender systems based on graph embedding techniques: A comprehensive review
• The Poisson Gamma Belief Network
• Nonparametric Bayesian Negative Binomial Factor Analysis
• Independent finite approximations for Bayesian nonparametric inference
• Dynamic Collaborative Filtering with Compound Poisson Factorization
• A Comparative Study of Gamma Markov Chains for Temporal Non-Negative Matrix Factorization
• A Nonparametric Bayesian Model for Sparse Dynamic Multigraphs
• Deep Poisson gamma dynamical systems
• Gamma Belief Networks
• Sequential Edge Clustering in Temporal Multigraphs