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