  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, enhancisng both theoretical
foundations and practical interpretability. Additionally, we extend our
framework to classification tasks as a preprocessing pipeline, showcasing its
versatility. Experimental evaluations on synthetic datasets as well as
real-world microbiome data demonstrate the superior performance of the PLN-Tree
model in capturing hierarchical dependencies and providing valuable insights
into complex data structures, showing the practical interest of knowledge
graphs like the taxonomy in ecosystems modeling.
