# Tree-based variational inference for Poisson log-normal models

arXiv: https://arxiv.org/abs/2406.17361 · HTML: https://mlsanity.com/paper/2406.17361/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 84 references that are in the map.
- First posted on arXiv 25 Jun 2024.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Learnable latent embeddings for joint behavioral and neural analysis](https://mlsanity.com/paper/2204.00673/) (2022)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICA](https://mlsanity.com/paper/2106.09620/) (2021)
- [Variational Boosting: Iteratively Refining Posterior Approximations](https://mlsanity.com/paper/1611.06585/) (2016)
- [Online Variational Filtering and Parameter Learning](https://mlsanity.com/paper/2110.13549/) (2021)
- [Variational Message Passing with Structured Inference Networks](https://mlsanity.com/paper/1803.05589/) (2018)
- [A General Method for Amortizing Variational Filtering](https://mlsanity.com/paper/1811.05090/) (2018)
- [Variational inference for sparse network reconstruction from count data](https://mlsanity.com/paper/1806.03120/) (2018)
- [A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution](https://mlsanity.com/paper/1609.00066/) (2016)
- [Variational inference for probabilistic Poisson PCA](https://mlsanity.com/paper/1703.06633/) (2017)
- [Zero-inflation in the Multivariate Poisson Lognormal Family](https://mlsanity.com/paper/2405.14711/) (2024)
- [Dirichlet-tree multinomial mixtures for clustering microbiome compositions](https://mlsanity.com/paper/2008.00400/) (2020)
- [Variational excess risk bound for general state space models](https://mlsanity.com/paper/2312.09607/) (2023)

## Built on by (most cited first, 2 of 2)

- [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)

When studying ecosystems, hierarchical trees are often used to organize entities based on proximity criteria, such as the taxonomy in microbiology, social classes in geography, or product types in retail businesses, offering valuable insights into entity relationships. Despite their significance, current count-data models do not leverage this structured information. In particular, the widely used Poisson log-normal (PLN) model, known for its ability to model interactions between entities from count data, lacks the possibility to incorporate such hierarchical tree structures, limiting its applicability in domains characterized by such complexities. To address this matter, we introduce the PLN-Tree model as an extension of the PLN model, specifically designed for modeling hierarchical count data. By integrating structured variational inference techniques, we propose an adapted training procedure and establish identifiability results, enhancing both theoretical foundations and practical interpretability. Experiments on synthetic datasets and human gut microbiome data highlight generative improvements when using PLN-Tree, demonstrating the practical interest of knowledge graphs like the taxonomy in microbiome modeling. Additionally, we present a proof-of-concept implication of the identifiability results by illustrating the practical benefits of using identifiable features for classification tasks, showcasing the versatility of the framework.