In this paper we introduce the literature on regression models with tensor variables and present a Bayesian linear model for inference, under the assumption of sparsity of the tensor coefficient. We exploit the CONDECOMP/PARAFAC (CP) representation for the tensor of coefficients in order to reduce the number of parameters and adopt a suitable hierarchical shrinkage prior for inducing sparsity. We propose a MCMC procedure via Gibbs sampler for carrying out the estimation, discussing the issues related to the initialisation of the vectors of parameters involved in the CP representation.
Billio, Monica; Casarin, Roberto; Iacopini, Matteo. (2018). Bayesian Tensor Regression Models. In Marco Corazza, María Durbán, Aurea Grané, Cira Perna, Marilena Sibillo (Eds.), Mathematical and Statistical Methods for Actuarial Sciences and Finance (pp. 159-163). Springer. Isbn: 978-3-319-89823-0. Doi: 10.1007/978-3-319-89824-7_28.
Bayesian Tensor Regression Models
Matteo Iacopini
2018
Abstract
In this paper we introduce the literature on regression models with tensor variables and present a Bayesian linear model for inference, under the assumption of sparsity of the tensor coefficient. We exploit the CONDECOMP/PARAFAC (CP) representation for the tensor of coefficients in order to reduce the number of parameters and adopt a suitable hierarchical shrinkage prior for inducing sparsity. We propose a MCMC procedure via Gibbs sampler for carrying out the estimation, discussing the issues related to the initialisation of the vectors of parameters involved in the CP representation.
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