Boosting multiplicative model combination

In this article, we define a new boosting-type algorithm for multiplicative model combination using as loss function the Hyvärinen scoring rule. In particular, we focus on density estimation problems and the aim is to define a suitable estimator, using a multiplicative combination of elementary density functions, which correspond to simplified or partially specified probability models for the interest random phenomenon. The boosting algorithm provides a simple sequential procedure for updating the weights of the component density functions, until an optimality criterion is satisfied. An extension of this procedure can be useful for composite likelihood inference, in order to specify the weights of the component likelihood objects and, simultaneously, implement parameter estimation. Finally, three applications are presented. The first one regards prediction and inference for autoregressive models, the second one is the use of model pools for prediction in a time series framework, and the third one is the estimation of the covariance and the precision matrices of a multivariate Gaussian distribution. Empirical results on real-world financial data are presented in challenging contexts, where we have to deal with a large dataset or with sparse matrices and a large number of unknown parameters.