# Zero-inflation in the Multivariate Poisson Lognormal Family

arXiv: https://arxiv.org/abs/2405.14711 · HTML: https://mlsanity.com/paper/2405.14711/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 46 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 6 of 6)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Variational inference for sparse network reconstruction from count data](https://mlsanity.com/paper/1806.03120/) (2018)
- [Variational inference for probabilistic Poisson PCA](https://mlsanity.com/paper/1703.06633/) (2017)
- [High-Dimensional Covariate-Augmented Overdispersed Poisson Factor Model](https://mlsanity.com/paper/2402.15071/) (2024)
- [Variational Auto-encoder Based Bayesian Poisson Tensor Factorization for Sparse and Imbalanced Count Data](https://mlsanity.com/paper/1910.05570/) (2019)
- [Composite likelihood inference for the Poisson log-normal model](https://mlsanity.com/paper/2402.14390/) (2024)

## Built on by (most cited first, 4 of 4)

- [Tree-based variational inference for Poisson log-normal models](https://mlsanity.com/paper/2406.17361/) (2024)
- [Semi-supervised Clustering Through Representation Learning of Large-scale EHR Data](https://mlsanity.com/paper/2505.20731/) (2025)
- [Independent Component Discovery in Temporal Count Data](https://mlsanity.com/paper/2601.21696/) (2026)
- [Understanding When Poisson Log-Normal Models Outperform Penalized Poisson Regression for Microbiome Count Data](https://mlsanity.com/paper/2604.03853/) (2026)

## Abstract (arXiv)

Analyzing high-dimensional count data is a challenge and statistical model-based approaches provide an adequate and efficient framework that preserves explainability. The (multivariate) Poisson-Log-Normal (PLN) model is one such model: it assumes count data are driven by an underlying structured latent Gaussian variable, so that the dependencies between counts solely stems from the latent dependencies. However PLN doesn't account for zero-inflation, a feature frequently observed in real-world datasets. Here we introduce the Zero-Inflated PLN (ZIPLN) model, adding a multivariate zero-inflated component to the model, as an additional Bernoulli latent variable. The Zero-Inflation can be fixed, site-specific, feature-specific or depends on covariates. We estimate model parameters using variational inference that scales up to datasets with a few thousands variables and compare two approximations: (i) independent Gaussian and Bernoulli variational distributions or (ii) Gaussian variational distribution conditioned on the Bernoulli one. The method is assessed on synthetic data and the efficiency of ZIPLN is established even when zero-inflation concerns up to 90% of the observed counts. We then apply both ZIPLN and PLN to a cow microbiome dataset, containing 90.6% of zeroes. Accounting for zero-inflation significantly increases log-likelihood and reduces dispersion in the latent space, thus leading to improved group discrimination.