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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References
Billio, M., Casarin, R., Iacopini, M.: Bayesian Dynamic Tensor Regression, arXiv preprint arXiv:1709.09606 (2017)
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Acknowledgements
This research has benefited from the use of the Scientific Computation System of Ca’ Foscari University of Venice (SCSCF) for the computational for the implementation of the inferential procedure.
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Billio, M., Casarin, R., Iacopini, M. (2018). Bayesian Tensor Regression Models. In: Corazza, M., Durbán, M., Grané, A., Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-89824-7_28
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DOI: https://doi.org/10.1007/978-3-319-89824-7_28
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