Consistent regression using data-dependent coverings

作     者：Margot, Vincent Baudry, Jean-Patrick Guilloux, Frederic Wintenberger, Olivier 

作者机构：Sorbonne Univ Lab Probabilites Stat & Modelisat Campus Pierre & Marie CurieTour 16-261er Etage F-75005 Paris France 

出 版 物：《ELECTRONIC JOURNAL OF STATISTICS》 (Electron. J. Stat.)

年 卷 期：2021年第15卷第1期

页      面：1743-1782页

核心收录：

主　　题：Consistency nonparametric regression rule-based algorithm data-dependent covering interpretable learning 

摘      要：We introduce a procedure to generate an estimator of the regression function based on a data-dependent quasi-covering of the feature space. A quasi-partition is generated from the quasi-covering and the estimator predicts the conditional empirical expectation over the cells of the quasi-partition. We provide sufficient conditions to ensure the consistency of the estimator. Each element of the quasi-covering is labeled as significant or insignificant. We avoid the condition of cell shrinkage commonly found in the literature for data-dependent partitioning estimators. This reduces the number of elements in the quasi-covering. An important feature of our estimator is that it is interpretable. The proof of the consistency is based on a control of the convergence rate of the empirical estimation of conditional expectations, which is interesting in itself.