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.
Bayesian Tensor Regression Models / Billio, Monica; Casarin, Roberto; Iacopini, Matteo. - (2018), pp. 159-163. [10.1007/978-3-319-89824-7]
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.File | Dimensione | Formato | |
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