High-Dimensional Longitudinal Classification with the Multinomial Fused Lasso

TL;DR

This paper introduces a regularized estimation method for high-dimensional longitudinal classification that produces piecewise constant coefficients over time, with an efficient algorithm and practical application to Alzheimer's disease data.

Contribution

It develops a novel approach combining lasso and fused lasso regularizers for longitudinal classification, with an efficient proximal gradient algorithm and real-world application.

Findings

Effective estimation of time-varying coefficients with change points

Application to Alzheimer's disease data demonstrates practical utility

Guidelines for tuning parameter selection and model stability assessment

Abstract

We study regularized estimation in high-dimensional longitudinal classification problems, using the lasso and fused lasso regularizers. The constructed coefficient estimates are piecewise constant across the time dimension in the longitudinal problem, with adaptively selected change points (break points). We present an efficient algorithm for computing such estimates, based on proximal gradient descent. We apply our proposed technique to a longitudinal data set on Alzheimer's disease from the Cardiovascular Health Study Cognition Study, and use this data set to motivate and demonstrate several practical considerations such as the selection of tuning parameters, and the assessment of model stability.