# Nonparametric Bayesian Factor Analysis for Dynamic Count Matrices

arXiv: https://arxiv.org/abs/1512.08996 · HTML: https://mlsanity.com/paper/1512.08996/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Dec 2015.

## Built on by (most cited first, 6 of 6)

- [Recommender systems based on graph embedding techniques: A comprehensive review](https://mlsanity.com/paper/2109.09587/) (2021)
- [Negative-Binomial Randomized Gamma Markov Processes for Heterogeneous Overdispersed Count Time Series](https://mlsanity.com/paper/2402.18995/) (2024)
- [Recurrent Coupled Topic Modeling over Sequential Documents](https://mlsanity.com/paper/2106.13732/) (2021)
- [Ordinal Graph Gamma Belief Network for Social Recommender Systems](https://mlsanity.com/paper/2209.05106/) (2022)
- [A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics](https://mlsanity.com/paper/2402.16297/) (2024)
- [Poisson-Gamma Dynamical Systems with Time-varying Transition Dynamics](https://mlsanity.com/paper/2609.00896/) (2026)

## Abstract (arXiv)

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.