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Title: Variational inference for sparse high-dimensional graphical-VAR models Authors:  Nicolas Bianco - University of Padua (Italy) [presenting]
Mauro Bernardi - University of Padova (Italy)
Daniele Bianchi - Queen Mary University of London (United Kingdom)
Abstract: The increased complexity of modern datasets requires suitable techniques to select the most relevant features and to carry out an accurate inference in a reasonable amount of time. We develop a variational approximation algorithm to deal with sparse estimation of high-dimensional graphical vector autoregressive models with the possibility of including some exogenous covariates. The purpose is two-fold. First, we exploit the product density factorisation of the joint variational density that leads to the mean-field paradigm as well as the representation of the problem as a sequence of auxiliary regressions that rely on the Cholesky factorisation of the precision matrix. Both the Normal-double-Gamma prior and the Spike and Slab prior are implemented to shrink toward zero both the autoregressive and the precision matrices. The second contribution concerns the solution of the lack-of-identification problem that relies on the employed Cholesky factorisation. We propose to approximate the marginal likelihood of each model permutation by the variational model evidence and to exploit it to get the MaP estimates of the model parameters. When the dimension of the model is large, the complete exploration of the permutations' space becomes unfeasible, hence a parallel interacting simulated annealing algorithm is used in this case.