Agenda

Speaker:
Roberto Casarin, Dipartimento di Economia

Abstract:
To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with little loss of information about the response. The method is flexible, allowing for tensor-wise, mode-wise, or combined random projections as special cases. A Bayesian inference framework is provided, featuring a hierarchical prior distribution and a low-rank parameter representation. Strong theoretical support is provided for the concentration properties of random projections and for the posterior consistency of 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 reverse logistic regression. An extensive simulation study is conducted to examine the effects of different tuning parameters. Simulations indicate, and real-data applications confirm, that compressed Bayesian tensor regressions can achieve better out-of-sample predictions while significantly reducing computational costs compared to standard Bayesian tensor regressions. 
Joint with R. Craiu and Q. Wang

Bio sketch:
Roberto Casarin is a Professor of Econometrics at Ca’ Foscari University of Venice, a position he has held since 2019, and has served as Director of the Venice Centre in Economic and Risk Analytics (VERA) since 2020. He is Co-chair of the European Society of Bayesian Econometrics (ESOBE), a lifetime member of the International Society for Bayesian Analysis (ISBA), Chair Elect of the EFaB section of ISBA, and a board member of the PhD program in Economics (SSE), the Master in Data Analytics for Business and Societies (DABS), and the Master in Quantum Machine Learning (QML). Previously, he served as Associate and Assistant Professor at Ca’ Foscari University of Venice and the University of Brescia, as an adjunct professor at the University of Trieste, as a research assistant at the University of Padova, and as a research fellow at GRETA Associates. He has also been a visiting scholar at the University of Toronto, Paris-Sud University, the University of Bristol, and Paris-Dauphine University.