# Microbiome subcommunity learning with logistic-tree normal latent Dirichlet allocation

arXiv: https://arxiv.org/abs/2109.05386 · HTML: https://mlsanity.com/paper/2109.05386/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 55 references that are in the map.
- First posted on arXiv 11 Sep 2021.

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

- [Graph-Sparse LDA: A Topic Model with Structured Sparsity](https://mlsanity.com/paper/1410.4510/) (2014)
- [A Direct Sampler for G-Wishart Variates](https://mlsanity.com/paper/1304.1350/) (2013)
- [Bayesian Analysis of Dynamic Linear Topic Models](https://mlsanity.com/paper/1511.03947/) (2015)
- [MIMIX: a Bayesian Mixed-Effects Model for Microbiome Data from Designed Experiments](https://mlsanity.com/paper/1703.07747/) (2017)
- [Bayesian graphical compositional regression for microbiome data](https://mlsanity.com/paper/1712.04723/) (2017)
- [A tree-based model for addressing sparsity and taxa covariance in microbiome compositional count data](https://mlsanity.com/paper/2106.15051/) (2021)

## Abstract (arXiv)

Mixed-membership (MM) models such as Latent Dirichlet Allocation (LDA) have been applied to microbiome compositional data to identify latent subcommunities of microbial species. These subcommunities are informative for understanding the biological interplay of microbes and for predicting health outcomes. However, microbiome compositions typically display substantial cross-sample heterogeneities in subcommunity compositions -- that is, the variability in the proportions of microbes in shared subcommunities across samples -- which is not accounted for in prior analyses. As a result, LDA can produce inference which is highly sensitive to the specification of the number of subcommunities and often divides a single subcommunity into multiple artificial ones. To address this limitation, we incorporate the logistic-tree normal (LTN) model into LDA to form a new MM model. This model allows cross-sample variation in the composition of each subcommunity around some "centroid" composition that defines the subcommunity. Incorporation of auxiliary P'olya-Gamma variables enables a computationally efficient collapsed blocked Gibbs sampler to carry out Bayesian inference under this model. By accounting for such heterogeneity, our new model restores the robustness of the inference in the specification of the number of subcommunities and allows meaningful subcommunities to be identified.