Sparsity-Promoting Bayesian Dynamic Linear Models

François Caron (1, 2) , Luke Bornn (3) , Arnaud Doucet (4)

1 ALEA - Advanced Learning Evolutionary Algorithms
2 IMB - Institut de Mathématiques de Bordeaux
3 UBC Statistics - Department of Statistics [Vancouver]
4 Department of Statistics [Oxford]

Sparsity-promoting priors have become increasingly popular over recent years due to an increased number of regression and classification applications involving a large number of predictors. In time series applications where observations are collected over time, it is often unrealistic to assume that the underlying sparsity pattern is fixed. We propose here an original class of flexible Bayesian linear models for dynamic sparsity modelling. The proposed class of models expands upon the existing Bayesian literature on sparse regression using generalized multivariate hyperbolic distributions. The properties of the models are explored through both analytic results and simulation studies. We demonstrate the model on a financial application where it is shown that it accurately represents the patterns seen in the analysis of stock and derivative data, and is able to detect major events by filtering an artificial portfolio of assets.

Mots clés: generalized hyperbolic; Gaussian mixture models; sparsity; dynamic regression; particle filters; particle MCMC

Domaines: Méthodologie [stat.ME]; Machine Learning [stat.ML]; Calcul [stat.CO]

François Caron, Luke Bornn, Arnaud Doucet. Sparsity-Promoting Bayesian Dynamic Linear Models. [Research Report] RR-7895, INRIA. 2012, pp.23. ⟨hal-00675274⟩