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

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).

Keywords:

• Random forest
• missing data
• consistency
• partial imputation

AMS Subject Classifications:

• 62G05
• 62G20

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Codes to reproduce our results can be found in https://github.com/IrvingGomez/RandomForestsSimulations.