# Nonparametric graphical model for counts

arXiv: https://arxiv.org/abs/1901.00886 · HTML: https://mlsanity.com/paper/1901.00886/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jan 2019.

## Built on by (most cited first, 7 of 7)

- [Generalised Bayesian Inference for Discrete Intractable Likelihood](https://mlsanity.com/paper/2206.08420/) (2022)
- [Scalable Bigraphical Lasso: Two-way Sparse Network Inference for Count Data](https://mlsanity.com/paper/2203.07912/) (2022)
- [An additive graphical model for discrete data](https://mlsanity.com/paper/2112.14674/) (2021)
- [Robust Score Matching](https://mlsanity.com/paper/2501.05105/) (2025)
- [Negative-Binomial Randomized Gamma Markov Processes for Heterogeneous Overdispersed Count Time Series](https://mlsanity.com/paper/2402.18995/) (2024)
- [Sparse Interaction Neighborhood Selection for Markov Random Fields via Reversible Jump and Pseudoposteriors](https://mlsanity.com/paper/2204.05933/) (2022)
- [Graphical estimation of multivariate count time series](https://mlsanity.com/paper/2302.08801/) (2023)

## Abstract (arXiv)

Although multivariate count data are routinely collected in many application areas, there is surprisingly little work developing flexible models for characterizing their dependence structure. This is particularly true when interest focuses on inferring the conditional independence graph. In this article, we propose a new class of pairwise Markov random field-type models for the joint distribution of a multivariate count vector. By employing a novel type of transformation, we avoid restricting to non-negative dependence structures or inducing other restrictions through truncations. Taking a Bayesian approach to inference, we choose a Dirichlet process prior for the distribution of a random effect to induce great flexibility in the specification. An efficient Markov chain Monte Carlo (MCMC) algorithm is developed for posterior computation. We prove various theoretical properties, including posterior consistency, and show that our COunt Nonparametric Graphical Analysis (CONGA) approach has good performance relative to competitors in simulation studies. The methods are motivated by an application to neuron spike count data in mice.