On the consistency of a random forest algorithm in the presence of missing entries

Irving Gómez-Méndez and Emilien Joly

Journal of Nonparametric Statistics, 2024, vol. 36, issue 2, 400-434

Abstract: This paper tackles the problem of constructing a nonparametric predictor when the latent variables are given with incomplete information. The convenient predictor for this task is the random forest algorithm in conjunction to the so-called CART criterion. The proposed technique enables a partial imputation of the missing values in the data set in a way that suits both a consistent estimator of the regression function as well as a partial recovery of the missing values. The imputation is done through iterative assignation of the missing values to the tree's cells, maximising the CART criterion. A proof of the consistency of the random forest estimator is given in the case where each latent variable is missing completely at random (MCAR).

Date: 2024
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DOI: 10.1080/10485252.2023.2219783

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