Gradient boosting for parsimonious additive covariance matrix modelling

Gradient boosting algorithms are attractive for effect selection in multi-parameter generalized additive models. Due to the high-dimensionality of the problem, a parsimonious covariance matrix model is required for modelling multivariate Gaussian data. Here, we address covariance matrix model specification using gradient boosting. In particular, the aim is ranking the effects used to model the elements of the modified Cholesky decomposition of the precision matrix. The performance of the proposal is illustrated on electricity demand data.