A0807
Title: Uncertainty quantification in Bayesian reduced-rank sparse regressions
Authors: Alexander Shestopaloff - Queen Mary University of London (United Kingdom) [presenting]
Abstract: Reduced-rank regression recognizes the possibility of a rank-deficient matrix of coefficients, which is particularly useful when the data is high-dimensional. A novel Bayesian model is proposed for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows for uncertainty quantification. The method employs a mixture prior to the regression coefficient matrix along with a global-local shrinkage prior to its low-rank decomposition. Then, the signal adaptive variable selector is relied onto 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.
