Bayesian Nonlinear Tensor Regression with Functional Fused Elastic Net Prior

TL;DR

This paper introduces a Bayesian nonlinear tensor regression model with a functional fused elastic net prior, effectively capturing spatial structure, nonlinearity, and discontinuities in tensor covariates for scalar response prediction.

Contribution

It develops a novel Bayesian additive regression framework with a functional fused elastic net prior to model complex spatial and nonlinear relationships in tensor data.

Findings

Demonstrates superior performance in simulations

Effectively detects spatial discontinuities

Provides interpretable results on facial data

Abstract

Tensor regression methods have been widely used to predict a scalar response from covariates in the form of a multiway array. In many applications, the regions of tensor covariates used for prediction are often spatially connected with unknown shapes and discontinuous jumps on the boundaries. Moreover, the relationship between the response and the tensor covariates can be nonlinear. In this article, we develop a nonlinear Bayesian tensor additive regression model to accommodate such spatial structure. A functional fused elastic net prior is proposed over the additive component functions to comprehensively model the nonlinearity and spatial smoothness, detect the discontinuous jumps, and simultaneously identify the active regions. The great flexibility and interpretability of the proposed method against the alternatives are demonstrated by a simulation study and an analysis on facial feature data.