Subspace decompositions for association structure learning in multivariate categorical response regression

TL;DR

This paper introduces a penalized likelihood approach using subspace decomposition to model and interpret complex associations among multiple categorical responses, improving flexibility and clarity in multivariate categorical data analysis.

Contribution

It proposes a novel subspace decomposition framework for multivariate categorical response regression, providing interpretability and theoretical guarantees in high-dimensional settings.

Findings

Effective modeling of mutual, joint, and conditional associations

Theoretical error bounds established for high-dimensional cases

Demonstrated improved interpretability and prediction accuracy

Abstract

Modeling the complex relationships between multiple categorical response variables as a function of predictors is a fundamental task in the analysis of categorical data. However, existing methods can be difficult to interpret and may lack flexibility. To address these challenges, we introduce a penalized likelihood method for multivariate categorical response regression that relies on a novel subspace decomposition to parameterize interpretable association structures. Our approach models the relationships between categorical responses by identifying mutual, joint, and conditionally independent associations, which yields a linear problem within a tensor product space. We establish theoretical guarantees for our estimator, including error bounds in high-dimensional settings, and demonstrate the method's interpretability and prediction accuracy through comprehensive simulation studies.