A likelihood-based approach for multivariate categorical response regression in high dimensions

TL;DR

This paper introduces a penalized likelihood approach for high-dimensional multivariate categorical response regression, enabling variable selection and interpretation, with demonstrated effectiveness through simulations and a cancer risk prediction application.

Contribution

It presents a novel penalized likelihood method for multivariate categorical regression, including an efficient algorithm and theoretical error bounds, extending to semi-supervised and multivariate cases.

Findings

Effective variable selection in high-dimensional settings

Improved interpretability and prediction accuracy

Validated through simulations and cancer risk prediction

Abstract

We propose a penalized likelihood method to fit the bivariate categorical response regression model. Our method allows practitioners to estimate which predictors are irrelevant, which predictors only affect the marginal distributions of the bivariate response, and which predictors affect both the marginal distributions and log odds ratios. To compute our estimator, we propose an efficient first order algorithm which we extend to settings where some subjects have only one response variable measured, i.e., the semi-supervised setting. We derive an asymptotic error bound which illustrates the performance of our estimator in high-dimensional settings. Generalizations to the multivariate categorical response regression model are proposed. Finally, simulation studies and an application in pan-cancer risk prediction demonstrate the usefulness of our method in terms of interpretability and prediction accuracy. An R package implementing the proposed method is available for download at github.com/ajmolstad/BvCategorical.