Tree-based variational inference for Poisson log-normal models

TL;DR

This paper introduces PLN-Tree, a hierarchical extension of the Poisson log-normal model that incorporates structured tree information into count data modeling, improving interpretability and generative performance.

Contribution

The paper develops PLN-Tree, a novel hierarchical model for count data that integrates structured variational inference and establishes identifiability, advancing microbiome and ecosystem data analysis.

Findings

Enhanced generative performance on synthetic and microbiome data

Improved interpretability through identifiable features

Practical benefits demonstrated in classification tasks

Abstract

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.