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Title: Bayesian Markov switching tensor regression for time-varying networks Authors:  Monica Billio - University of Venice (Italy)
Roberto Casarin - University Ca' Foscari of Venice (Italy)
Matteo Iacopini - Ca Foscari University of Venice (Italy) [presenting]
Abstract: A new Bayesian Markov switching regression model is proposed for multi-dimensional arrays (tensors) of binary time series. We assume a zero-inflated logit dynamics with timevarying parameters and apply it to multi-layer temporal networks. The aim is threefold. First, in order to avoid over-fitting we propose a parsimonious parametrization of the model, based on a low-rank decomposition of the tensor of regression coefficients. Second, the parameters of the tensor model are driven by a hidden Markov chain, thus allowing for structural changes. The regimes are identified through prior constraints on the mixing probability of the zero-inflated model. Finally, we model the jointly dynamics of the network and of a set of variables of interest. We follow a Bayesian approach to inference, exploiting the Polya-Gamma data augmentation scheme for logit models in order to provide an efficient Gibbs sampler for posterior approximation. We show the effectiveness of the sampler on simulated datasets of medium-big sizes, finally we apply the methodology to a real dataset of financial networks.