Abstract:
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Random forests have proven themselves 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 the scale of random forest errors. In this paper, we analyze a random forest model based 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 (2013). In other words, our results let us both characterize and estimate the error-distribution of random forest predictions. Thus, random forests need not only be treated as black-box predictive algorithms, and can also be used for statistical inference.
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