The Shapley effects are global sensitivity indices: they quantify the impact of each input variable on the output variable in a model. In this work, we suggest new estimators of these sensitivity indices. When the input distribution is known, we investigate the already existing estimator defined in [SNS16] and suggest a new one with a lower variance. Then, when the distribution of the inputs is unknown, we extend these estimators. We provide asymptotic properties of the estimators studied in this article. We also apply one of these estimators to a real data set.

Recursive partitioning methods are among the most popular techniques in machine learning. The purpose of this paper is to investigate how to adapt this methodology to the bipartite ranking problem. ), we present tree-structured algorithms designed for learning to rank instances based on classification data. The main contributions of the present work are the following: the practical implementation of the TREERANK algorithm, well-founded solutions to the crucial issues related to the splitting rule and the choice of the "right" size for the ranking tree. From the angle embraced in this paper, splitting is viewed as a cost-sensitive classification task with data-dependent cost. Hence, up to straightforward modifications, any classification algorithm may serve as a splitting rule. Also, we propose to implement a cost-complexity pruning method after the growing stage in order to produce a "right-sized" ranking sub-tree with large AUC. In particular, performance bounds are established for pruning schemes inspired by recent work on nonparametric model selection. Eventually, we propose indicators for variable importance and variable dependence, plus various simulation studies illustrating the potential of our method.