Model selection consists in comparing several candidate models according to a metric to be optimized. The process often involves a grid search, or such, and cross-validation, which can be time consuming, as well as not providing much information about the dataset itself. In this paper we propose a method to reduce the scope of exploration needed for the task. The idea is to quantify how much it would be necessary to depart from trained instances of a given family, reference models (RMs) carrying `rigid' decision boundaries (e.g. decision trees), so as to obtain an equivalent or better model. In our approach, this is realized by progressively relaxing the decision boundaries of the initial decision trees (the RMs) as long as this is beneficial in terms of performance measured on an analyzed dataset. More specifically, this relaxation is performed by making use of a neural decision tree, which is a neural network built from DTs. The final model produced by our method carries non-linear decision boundaries. Measuring the performance of the final model, and its agreement to its seeding RM can help the user to figure out on which family of models he should focus on.

We present a novel instance based approach to handle regression tasks in the context of supervised domain adaptation. The approach developed in this paper relies on the assumption that the task on the target domain can be efficiently learned by adequately reweighting the source instances during training phase. We introduce a novel formulation of the optimization objective for domain adaptation which relies on a discrepancy distance characterizing the difference between domains according to a specific task and a class of hypotheses. To solve this problem, we develop an adversarial network algorithm which learns both the source weighting scheme and the task in one feed-forward gradient descent. We provide numerical evidence of the relevance of the method on public datasets for domain adaptation through reproducible experiments accessible via an online demo interface.

A new procedure to construct predictive models in supervised learning problems by paying attention to the clustering structure of the input data is introduced. We are interested in situations where the input data consists of more than one unknown cluster, and where there exist different underlying models on these clusters. Thus, instead of constructing a single predictive model on the whole dataset, we propose to use a K-means clustering algorithm with different options of Bregman divergences, to recover the clustering structure of the input data. Then one dedicated predictive model is fit per cluster. For each divergence, we construct a simple local predictor on each observed cluster. We obtain one estimator, the collection of the K simple local predictors, per divergence, and we propose to combine them in a smart way based on a consensus idea. Several versions of consensual aggregation in both classification and regression problems are considered. A comparison of the performances of all constructed estimators on different simulated and real data assesses the excellent performance of our method. In a large variety of prediction problems, the consensual aggregation procedure outperforms all the other models.

In this paper, we introduce a new learning strategy based on a seminal idea of Mojirsheibani (1999, 2000, 2002a, 2002b), who proposed a smart method for combining several classifiers, relying on a consensus notion. In many aggregation methods, the prediction for a new observation x is computed by building a linear or convex combination over a collection of basic estimators r1(x),. .. , rm(x) previously calibrated using a training data set. Mojirsheibani proposes to compute the prediction associated to a new observation by combining selected outputs of the training examples. The output of a training example is selected if some kind of consensus is observed: the predictions computed for the training example with the different machines have to be "similar" to the prediction for the new observation. This approach has been recently extended to the context of regression in Biau et al. (2016). In the original scheme, the agreement condition is actually required to hold for all individual estimators, which appears inadequate if there is one bad initial estimator. In practice, a few disagreements are allowed ; for establishing the theoretical results, the proportion of estimators satisfying the condition is required to tend to 1. In this paper, we propose an alternative procedure, mixing the previous consensus ideas on the predictions with the Euclidean distance computed between entries. This may be seen as an alternative approach allowing to reduce the effect of a possibly bad estimator in the initial list, using a constraint on the inputs. We prove the consistency of our strategy in classification and in regression. We also provide some numerical experiments on simulated and real data to illustrate the benefits of this new aggregation method. On the whole, our practical study shows that our method may perform much better than the original combination technique, and, in particular, exhibit far less variance. We also show on simulated examples that this procedure mixing inputs and outputs is still robust to high dimensional inputs.

We focus on wind power modeling using machine learning techniques. We show on real data provided by the wind energy company Ma{\"i}a 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.