We wish to estimate conditional density using Gaussian Mixture Regression model with logistic weights and means depending on the covariate. We aim at selecting the number of components of this model as well as the other parameters by a penalized maximum likelihood approach. We provide a lower bound on penalty, proportional up to a logarithmic term to the dimension of each model, that ensures an oracle inequality for our estimator. Our theoretical analysis is supported by some numerical experiments.

Abstract. We focus on wind power modeling using machine learning techniques. We show on real data provided by the wind energy company Maïa Eolis, that parametric models, even following closely the physical equation relating wind production to wind speed are outperformed by intelligent learning algorithms. In particular, the CART-Bagging algorithm gives very stable and promising results. Besides, as a step towards forecast, we quantify the impact of using deteriorated wind measures on the performances. We show also on this application that the default methodology to select a subset of predictors provided in the standard random forest package can be refined, especially when there exists among the predictors one variable which has a major impact.

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Aggregating estimators using exponential weights depending on their risk appears optimal in expectation but not in probability. We use here a slight overpenalization to obtain oracle inequality in probability for such an explicit aggregation procedure. We focus on the fixed design regression framework and the aggregation of affine estimators and obtain results for a large family of affine estimators under a non necessarily independent sub-Gaussian noise assumptions.