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Factor Augmented Matrix Regression
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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.
Forward citations
Cited by 2 Pith papers
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Binary Response Forecasting under a Factor-Augmented Framework
A factor-augmented probit model with PCA-estimated factors yields consistent MLEs and improved U.S. recession forecasts versus standard probit.
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Feature Augmentations for High-Dimensional Learning
Adding PCA factors extracted from transformed input matrices (interactions, kernels, neural network hidden layers) to the original features improves out-of-sample prediction in many high-dimensional learning tasks.
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