Variational bayesian inference for sparsehigh–dimensional graphical–VAR models

• Nicolas Bianco ^[2] ; Mauro Ignacio Bernardi ; Daniele Bianchi ^[1]
  1. [1] Queen Mary University of London

     Queen Mary University of London

     Reino Unido

     
  2. [2] University of Padova
• Localización: Proceedings of the 35th International Workshop on Statistical Modelling : July 20-24, 2020 Bilbao, Basque Country, Spain / Itziar Irigoien Garbizu (ed. lit.), Dae-Jin Lee (ed. lit.), Joaquín Martínez Minaya (ed. lit.), María Xosé Rodríguez Álvarez (ed. lit.), 2020, ISBN 978-84-1319-267-3, págs. 19-24
• Idioma: inglés
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• Resumen

  • We develop a variational approximation method to deal with sparse estimation of high–dimensional graphical vector autoregressive models. The purpose of the project 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. A Normal–double– Gamma prior is imposed to shrink toward zero both the autoregression and the precision parameters. 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 (ELBO) and to exploit it to get MaP estimates of the model parameters. To explore the space of permutations, when the dimension of the model is large, we develop a new parallel collapsed simulated annealing algorithm (PCSA).