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 (features), detail methods to robustly estimate periodic light-curve features, introduce treeensemble 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%. 5 High-precision photometry missions (Kepler, MOST, CoRoT, etc.) are already challenging the theoretical understanding of the origin of variability and the connection of some specific sources to established classes of variables. 6 General Catalog of Variable Stars, http://www.sai.msu.su/groups/cluster/gcvs/gcvs/ 7 Not discussed herein are the challenges associated with discovery of variability. See Shin et al. (2009) for a review.

Nine Type Ia supernovae (SNe Ia) with preexisting Hubble Space Telescope (HST) data on their host galaxies have been close enough (within 25 Mpc) to search for a progenitor (Supplementary Table 1). No progenitor system has been found; only upper limits have been possible 31,8,9,10 . Limits range from M g = −3.9 mag in the case of SN 2004W to M I = −8.3 mag for SN 2003cg 31 . These limits provided only poor constraints; in the case of SN 2006dd and SN 2006mr in NGC 1316, they ruled out normal stars with initial masses greater than 6 M at the tip of the asymptotic giant branch (AGB), young post-AGB stars with initial masses greater than 4 M , and post-red-giant stars with initial masses greater than 9 M 8 .

We have publicly released a blinded mix of simulated SNe, with types (Ia, Ib, Ic, II) selected in proportion to their expected rate. The simulation is realized in the griz filters of the Dark Energy Survey (DES) with realistic observing conditions (sky noise, point spread function and atmospheric transparency) based on years of recorded conditions at the DES site. Simulations of non-Ia type SNe are based on spectroscopically confirmed light curves that include unpublished non-Ia samples donated from the Carnegie Supernova Project (CSP), the Supernova Legacy Survey (SNLS), and the Sloan Digital Sky Survey-II (SDSS-II). We challenge scientists to run their classification algorithms and report a type for each SN. A spectroscopically confirmed subset is provided for training. The goals of this challenge are to (1) learn the relative strengths and weaknesses of the different classification algorithms, (2) use the results to improve classification algorithms, and ( 3) understand what spectroscopically confirmed sub-sets are needed to properly train these algorithms. The challenge is available at www.hep.anl.gov/SNchallenge, and the due date for classifications is May 1, 2010.

The rate of image acquisition in modern synoptic imaging surveys has already begun to outpace the feasibility of keeping astronomers in the real-time discovery and classification loop. Here we present the inner workings of a framework, based on machine-learning algorithms, that captures expert training and ground-truth knowledge about the variable and transient sky to automate 1) the process of discovery on image differences and, 2) the generation of preliminary science-type classifications of discovered sources. Since follow-up resources for extracting novel science from fast-changing transients are precious, self-calibrating classification probabilities must be couched in terms of efficiencies for discovery and purity of the samples generated. We estimate the purity and efficiency in identifying real sources with a two-epoch image-difference discovery algorithm for the Palomar Transient Factory (PTF) survey. Once given a source discovery, using machine-learned classification trained on PTF data, we distinguish between transients and variable stars with a 3.8% overall error rate (with 1.7% errors for imaging within the Sloan Digital Sky Survey footprint). At >96% classification efficiency, the samples achieve 90% purity. Initial classifications are shown to rely primarily on context-based features, determined from the data itself and external archival databases. In the ∼one year since autonomous operations, this discovery and classification framework has led to several significant science results, from outbursting young stars to subluminous Type IIP supernovae to candidate tidal disruption events. We discuss future directions of this approach, including the possible roles of crowdsourcing and the scalability of machine learning to future surveys such a the Large Synoptical Survey Telescope (LSST).

With growing data volumes from synoptic surveys, astronomers necessarily must become more abstracted from the discovery and introspection processes. Given the scarcity of follow-up resources, there is a particularly sharp onus on the frameworks that replace these human roles to provide accurate and wellcalibrated probabilistic classification catalogs. Such catalogs inform the subsequent follow-up, allowing consumers to optimize the selection of specific sources for further study and permitting rigorous treatment of purities and efficiencies for population studies. Here, we describe a process to produce a probabilistic classification catalog of variability with machine learning from a multi-epoch photometric survey. In addition to producing accurate classifications, we show how to estimate calibrated class probabilities, and motivate the importance of probability calibration. We also introduce a methodology for feature-based anomaly detection, which allows discovery of objects in the survey that do not fit within the predefined class taxonomy. Finally, we apply these methods to sources observed by the All Sky Automated Survey (ASAS), and unveil the Machine-learned ASAS Classification Catalog (MACC), which is a 28-class probabilistic classification catalog of 50,124 ASAS sources. We estimate that MACC achieves a sub-20% classification error rate, and demonstrate that the class posterior probabilities are reasonably calibrated. MACC classifications compare favorably to the classifications of several previous domain-specific ASAS papers and to the -2 -ASAS Catalog of Variable Stars, which had classified only 24% of those sources into one of 12 science classes. The MACC is publicly available on-line.