Zeny Feng, University of Guelph

Title: Regularized Regression Models for Compositional Count Data Beyond the Multinomial

Date: Friday, October 23rd, 2026
Time: 1:30PM (PDT)
Location: AQ 3003

Abstract:  Compositional data in the form of taxonomical counts are prevalent in many biological fields, including ecology and microbiology. For example, benthic macroinvertebrate can be classified into taxonomical ranks from phylum to species. At a given rank, counts for (D) taxa can be treated as multivariate count (MVC) outcomes conditional on their total, with the multinomial distribution being a common choice. However, it cannot accommodate overdispersion, which is common in compositional data. Alternative multivariate count (MVC) models, including the Dirichlet-multinomial (DM), negative multinomial (NM), and generalized Dirichlet multinomial (GDM) models, can be used.  

In the present of p covariates, fitting these regression models is challenging because they fall outside the exponential family and may involve pD or more coefficient parameters. When p is large, we proposed a sparse group lasso approach to regularize MVC regression models and develop majorization-minimization (MM) algorithms to optimize the resulting models, using dominating hyperplane regularization (DHR) to majorize the penalty terms.  

To account for hierarchical relationships among taxa across taxonomic ranks, we consider the Dirichlet-tree multinomial (DTM) regression and propose two tree-guided penalty functions for regularizing DTM regression: the tree-guided sparse group lasso and the tree-guided hierarchical lasso. The complexity of these model present additional model fitting challenges, which are further exacerbated by the need of regularization. We extend the MM-algorithm developed for the regularized DM regression to accommodate the regularized DTM regression with two tree-guided penalty options. Simulation studies and real data analyses demonstrate the performance and practical applications of the proposed methods.