On the consistency of a random forest algorithm in the presence of missing entries
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This paper tackles the problem of constructing a non-parametric 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 estimation of the regression function as well as a probabilistic recovery of the missing values. A proof of the consistency of the random forest estimator that also simplifies the previous proofs of the classical consistency is given in the case where each latent variable is missing completely at random (MCAR).
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