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With the coming data deluge from synoptic surveys, there is a growing needfor frameworks that can quickly and automatically produce calibratedclassification probabilities for newly-observed variables based on a smallnumber of time-series measurements. In this paper, we introduce a methodologyfor variable-star classification, drawing from modern machine-learningtechniques. We describe how to homogenize the information gleaned from lightcurves by selection and computation of real-numbered metrics ("feature"),detail methods to robustly estimate periodic light-curve features, introducetree-ensemble methods for accurate variable star classification, and show howto rigorously evaluate the classification results using cross validation. On a25-class data set of 1542 well-studied variable stars, we achieve a 22.8%overall classification error using the random forest classifier; thisrepresents a 24% improvement over the best previous classifier on these data.This methodology is effective for identifying samples of specific scienceclasses: for pulsational variables used in Milky Way tomography we obtain adiscovery efficiency of 98.2% and for eclipsing systems we find an efficiencyof 99.1%, both at 95% purity. We show that the random forest (RF) classifier issuperior to other machine-learned methods in terms of accuracy, speed, andrelative immunity to features with no useful class information; the RFclassifier can also be used to estimate the importance of each feature inclassification. Additionally, we present the first astronomical use ofhierarchical classification methods to incorporate a known class taxonomy inthe classifier, which further reduces the catastrophic error rate to 7.8%.Excluding low-amplitude sources, our overall error rate improves to 14%, with acatastrophic error rate of 3.5%.

On Machine-Learned Classification of Variable Stars with Sparse and Noisy Time-Series Data