Autoreplicative random forests with applications to missing value imputation

Missing values are a common problem in data science and machine learning. Removing instances with missing values is a straightforward workaround, but this can significantly hinder subsequent data analysis, particularly when features outnumber instances. There are a variety of methodologies proposed in the literature for imputing missing values. Denoising Autoencoders, for example, have been leveraged efficiently for imputation. However, neural network approaches have been relatively less effective on smaller datasets. In this work, we propose Autoreplicative Random Forests (ARF) as a multi-output learning approach, which we introduce in the context of a framework that may impute via either an iterative or procedural process. Experiments on several low- and high-dimensional datasets show that ARF is computationally efficient and exhibits better imputation performance than its competitors, including neural network approaches. In order to provide statistical analysis and mathematical background to the proposed missing value imputation framework, we also propose probabilistic ARFs, where the confidence values are provided over different imputation hypotheses, therefore maximizing the utility of such a framework in a machine-learning pipeline targeting predictive performance.