Title

Structures Learning in Multivariate Categorical Response Regression.

Abstract

A novel framework for learning association structures in multivariate categorical response regression via subspace decomposition is proposed. By reparameterizing the model parameters through a carefully designed orthonormal basis, the proposed method unifies the modeling of complex dependencies, including mutual, joint, and conditional independence, among the response variables. The basis functions capture interactions of different orders, offering enhanced interpretability.

Penalized likelihood estimation is introduced, employing group lasso and overlapping group lasso penalties on the reparameterized coefficients to encourage hierarchical sparsity. An accelerated proximal gradient descent algorithm is developed for efficient optimization. Theoretical analysis provides an error bound for the estimator in high-dimensional settings, leveraging a restricted strong convexity condition that incorporates the Rademacher complexity.

The proposed framework advances the understanding and modeling of complex relationships in multivariate categorical data. It offers a structured approach to identify interpretable association patterns, enhancing model flexibility and scalability. The method's strong theoretical guarantees and empirical performance make it a valuable tool for analyzing categorical response data in various application domains.        

Bio

Hongru Zhao is a Ph.D. student in Statistics at the University of Minnesota, advised by Adam J. Rothman. His research interests lie in multivariate analysis, high-dimensional statistics, deep learning theory, statistical and machine learning, sequential analysis, distributed inference, random matrix theory, and nonconvex minimization. Hongru has co-authored several manuscripts, including a work in progress with Aaron J. Molstad and Adam J. Rothman on learning association structures in multivariate categorical response regression.