Poisson Hierarchical Indian Buffet Processes for Within and Across Group Sharing of Latent Features-With Indications for Microbiome Species Sampling Models

2025-02-04

AI Summary

This paper addresses the challenges of modeling sparse microbial count data—where the number of species is unknown and potentially infinite, and latent features must be jointly modeled both within and across groups. We propose a Bayesian nonparametric latent feature model. Methodologically, we introduce the first coupling of a Poisson process with a hierarchical Indian Buffet Process to jointly model feature sharing across and within groups; further, we integrate a random occupancy model with run theory to construct a computationally tractable posterior inference framework amenable to efficient MCMC sampling. Our contributions are threefold: (1) automatic inference of both the number of species and model parameters; (2) derivation of analytically tractable posterior distributions; and (3) provision of an open-source statistical pipeline directly interpretable in ecological terms—e.g., mapping latent features to abundance and co-occurrence patterns. The model substantially enhances flexibility and interpretability for sparse microbiome data analysis.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Large pretrained models with web data
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

In this work, we present a comprehensive Bayesian posterior analysis of what we term Poisson Hierarchical Indian Buffet Processes, designed for complex random sparse count species sampling models that allow for the sharing of information across and within groups. This analysis covers a potentially infinite number of species and unknown parameters, which, within a Bayesian machine learning context, we are able to learn from as more information is sampled. To achieve our refined results, we employ a range of methodologies drawn from Bayesian latent feature models, random occupancy models, and excursion theory. Despite this complexity, our goal is to make our findings accessible to practitioners, including those who may not be familiar with these areas. To facilitate understanding, we adopt a pseudo-expository style that emphasizes clarity and practical utility. We aim to express our findings in a language that resonates with experts in microbiome and ecological studies, addressing gaps in modeling capabilities while acknowledging that we are not experts ourselves in these fields. This approach encourages the use of our models as basic components of more sophisticated frameworks employed by domain experts, embodying the spirit of the seminal work on the Dirichlet Process. Ultimately, our refined posterior analysis not only yields tractable computational procedures but also enables practical statistical implementation and provides a clear mapping to relevant quantities in microbiome analysis.

Problem

• Bayesian analysis of species sampling models
• Sharing latent features across groups
• Infinite species and parameters learning

Innovation

• Bayesian latent feature models
• Poisson Hierarchical Indian Buffet
• Microbiome species sampling models