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When the methods of bagging or random forests are used for classification, an ensemble of t=1,2,... randomized classifiers is generated, and the predictions of the classifiers are aggregated by voting. Due to the randomization in these methods, there is a natural tradeoff between statistical performance and computational cost. On one hand, as t increases, the (random) prediction error of the ensemble tends to decrease and stabilize. On the other hand, larger ensembles require greater computational cost for training and making new predictions. In this talk, I will discuss some recent methods and theoretical results that quantify this tradeoff in a precise sense.