Asymptotic Theory for Random Forests
This work addresses the problem of making random forests usable for statistical inference rather than just black-box prediction, which is significant for statisticians and data scientists, though it is incremental as it builds on existing consistency results.
The paper tackles the lack of practical error estimates for random forests by analyzing a subsampling-based model, showing that predictions are asymptotically normal under specific scaling conditions and that the variance can be consistently estimated using an infinitesimal jackknife method.
Random forests have proven to be reliable predictive algorithms in many application areas. Not much is known, however, about the statistical properties of random forests. Several authors have established conditions under which their predictions are consistent, but these results do not provide practical estimates of random forest errors. In this paper, we analyze a random forest model based on subsampling, and show that random forest predictions are asymptotically normal provided that the subsample size s scales as s(n)/n = o(log(n)^{-d}), where n is the number of training examples and d is the number of features. Moreover, we show that the asymptotic variance can consistently be estimated using an infinitesimal jackknife for bagged ensembles recently proposed by Efron (2014). In other words, our results let us both characterize and estimate the error-distribution of random forest predictions, thus taking a step towards making random forests tools for statistical inference instead of just black-box predictive algorithms.