SDS Seminar Series – Shuangjie Zhang, University of Texas at Austin

The Fall 2026 SDS Seminar Series kicks off on September 11th from 2:00 p.m. to 3:00 p.m. with postdoctoral fellow Shuangjie Zhang (postdoctoral fellow, Department of Statistics & Data Science, UT Austin0. This event is in-person in the Avaya Room (POB 2.302).    

Title: Structure Learning for Directed Trees with Zero-Inflated Compositional Nodes

Abstract: Zero-inflated compositional data, which are vectors of proportions constrained to the probability simplex, arise frequently in modern applications, such as microbiome relative abundances across body sites. While regression methods for zero-inflated compositional data are well developed, no existing graphical model framework addresses the problem of learning conditional dependence structures among multiple compositional vectors. This paper introduces a novel framework for directed tree structure learning over compositional nodes. We employ the Kullback–Leibler divergence as the scoring function and model the conditional expectation of each child composition as a mixture of a baseline composition and a parent-driven component parameterized by a column-stochastic transition matrix. This formulation respects the simplex geometry, handles zero-inflated compositions gracefully, and, combined with a non-degeneracy condition on the transition matrix, ensures identifiability of edge directions from observational data. We prove consistency of structure recovery and derive finite-sample guarantees that characterize the required sample size in terms of the signal gap, node dimension, and penalty level. The efficacy of our approach is demonstrated through simulations and applications to multi-site microbiome data and single-cell data, yielding interpretable directed structures that partially align with known biological mechanisms.