B1739
Title: A Bayesian nonlinear 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 nonlinear tensor regression model is proposed, which allows for model instability and accounts for multi-dimensional array data. Regarding model instability, the parameters are assumed to be time-varying and are driven by latent processes to address structural breaks in the data. Regarding high dimensionality, the Soft PARAFAC strategy is followed to achieve dimensionality reduction while preserving the structural information between the covariates. Modified multi-way shrinkage prior is further imposed to address over-parametrization issues. An efficient MCMC algorithm that adopts random scan Gibbs within a back-fitting strategy is developed to achieve better scalability of the posterior approximation. The performance of the MCMC algorithm is demonstrated using synthetic datasets in simulation studies. Real-world applications are used to test the proposed model against the benchmark Lasso regression, where the model delivers superior performance.
