Bayesian Markov Switching Tensor Regression For Time-Varying Networks

Abstract

We propose a new Bayesian Markov switching regression model for multi-dimensional arrays (tensors) of binary time series. We assume a zero-inflated logit dynamics with time-varying parameters and apply it to multi-layer temporal networks. The original contribution 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 Pólya-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.

Keywords: Tensor calculus, tensor decomposition, latent variables, Bayesian statistics, hierarchical prior, networks, zero-inflated model, time series, financial networks

JEL Classification: C13, C33, C51, C53