On a low-rank matrix single index model

TL;DR

This paper provides a theoretical analysis of a low-rank matrix single index model, using PAC-Bayesian bounds to understand the joint estimation of the link function and coefficient matrix.

Contribution

It introduces a PAC-Bayesian approach to analyze the theoretical properties of joint estimation in the model, advancing understanding in biostatistics applications.

Findings

PAC-Bayesian bounds established for the model

Theoretical guarantees for joint estimation

Insights into estimation accuracy and convergence

Abstract

In this paper, we present a theoretical study of a low-rank matrix single index model. This model is recently introduced in biostatistics however its theoretical properties on estimating together the link function and the coefficient matrix are not yet carried out. Here, we advance on using PAC-Bayesian bounds technique to provide a rigorous theoretical understanding for jointly estimation of the link function and the coefficient matrix.