A0686
Title: Bayesian compressed tensor regression
Authors: Qing Wang - Ca Foscari University (Italy) [presenting]
Roberto Casarin - University Ca' Foscari of Venice (Italy)
Radu Craiu - University of Toronto (Canada)
Abstract: A new dimensionality reduction technique is proposed to address the common problem of high dimensionality in tensor regressions. A generalized tensor random projection method is introduced that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of information about the responses. The method is flexible, allowing for tensor-wise, mode-wise, or combined random projections as special cases. A Bayesian inference framework is provided featuring the use of a hierarchical prior distribution and a low-rank representation of the parameter. Strong theoretical support is provided for the concentration properties of the random projection and posterior consistency of the Bayesian inference. An efficient Gibbs sampler is developed to perform inference on the compressed data. To mitigate the sensitivity introduced by random projections, Bayesian model averaging is employed, with normalizing constants estimated using reversed logistic regression. An extensive simulation study is conducted to examine the effects of different tuning parameters. A real data application demonstrates that compressed Bayesian tensor regression achieves better out-of-sample prediction while significantly reducing computational cost compared to standard Bayesian tensor regression.
