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arXiv · 2306.01521

Uncertainty Quantification in Bayesian Reduced-Rank Sparse Regressions

Maria F. Pintado·Matteo Iacopini·Luca Rossini·Alexander Y. Shestopaloff
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Abstract

Reduced-rank regression recognises the possibility of a rank-deficient matrix of coefficients. We propose a novel Bayesian model for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows for uncertainty quantification. Our method employs a mixture prior on the regression coefficient matrix along with a global-local shrinkage prior on its low-rank decomposition. Then, we rely on the Signal Adaptive Variable Selector to perform sparsification and define two novel tools: the Posterior Inclusion Probability uncertainty index and the Relevance Index. The validity of the method is assessed in a simulation study, and then its advantages and usefulness are shown in real-data applications on the chemical composition of tobacco and on the photometry of galaxies.

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Maria F. Pintado, Matteo Iacopini, Luca Rossini, Alexander Y. Shestopaloff. 2023-06-02. Uncertainty Quantification in Bayesian Reduced-Rank Sparse Regressions. https://arxiv.org/abs/2306.01521

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