Factor Augmented Matrix Regression

TL;DR

This paper introduces FAMAR, a novel method for matrix-variate data analysis that efficiently estimates factors and loadings, improving accuracy and interpretability in high-dimensional economic datasets.

Contribution

FAMAR provides a new non-iterative algorithm for factor estimation and an accelerated penalized regression approach, with proven convergence properties.

Findings

FAMAR outperforms existing methods in accuracy and speed.

It effectively captures economic factors influencing GDP.

Empirical results validate its interpretability and efficiency.

Abstract

We introduce \underline{F}actor-\underline{A}ugmented \underline{Ma}trix \underline{R}egression (FAMAR) to address the growing applications of matrix-variate data and their associated challenges, particularly with high-dimensionality and covariate correlations. FAMAR encompasses two key algorithms. The first is a novel non-iterative approach that efficiently estimates the factors and loadings of the matrix factor model, utilizing techniques of pre-training, diverse projection, and block-wise averaging. The second algorithm offers an accelerated solution for penalized matrix factor regression. Both algorithms are supported by established statistical and numerical convergence properties. Empirical evaluations, conducted on synthetic and real economics datasets, demonstrate FAMAR's superiority in terms of accuracy, interpretability, and computational speed. Our application to economic data showcases how matrix factors can be incorporated to predict the GDPs of the countries of interest, and the influence of these factors on the GDPs.