tokens: forest algorithm (TPC), while the probability estimates of our ConvNet model appear to be better calibrated. When the same network architecture is applied to the SDSS data set, the network fails to outperform TPC, but the probabilities are still slightly better calibrated. The major advantage of ConvNets is that useful features are learned automatically from images, while traditional machine learning algorithms require feature engineering as a separate process to produce accurate classifications. ConvNets have recently achieved record-breaking results in many image classification tasks (LeCun et al. 2015 ) and have been quickly and widely adopted by the computer vision community. One of the main reasons for the success is that ConvNets are general-purpose algorithms that are applicable to a variety of problems without the need for designing a feature extractor. The lack of requirement for feature extraction is a huge advantage, e.g. when the task is to classify 1000 classes in the ImageNet data set (Russakovsky et al. 2015 ), as a good feature extractor for identifying images of cats would be of little use for classifying sailboats, and it is impractical to design a separate feature extractor for each class. However, when there already exists a good feature extractor for the problem at hand, e.g. the concentration parameter, the weight-averaged spread_model parameter from DES (Desai et al. 2012 ; Crocce et al. 2016 ), or even the SE xtractor software, conventional machine learning algorithms that have been shown to be effective, such as TPC (Carrasco Kind Brunner 2013 ; Kim et al. 2015 ), remain a viable option. As the ‘no free lunch’ theorem (Wolpert 1996 ) states, there is no model that works for every problem. For the CFHTLenS data set, our ConvNet model outperforms TPC. Since the SDSS catalogue provides the concentration parameter that is highly optimized for star–galaxy classification, TPC works better for SDSS. Although we used various techniques to combat overfitting, it is possible that our ConvNet model has overfit the data. Overfitting could explain why our ConvNet model with maximal information fails to significantly outperform a standard machine learning algorithm that uses the reduced summary information from catalogues. The most effective way to prevent overfitting would be to simply collect more training images with spectroscopic follow-up, as the performance of ConvNets generally improves with more training data. However, spectroscopic observations are expensive and time-consuming, and it is unclear if sufficient training data will be available in future photometric surveys. If enough training data become available in DES or LSST, ConvNets become an attractive option because it can be applied immediately on reduced, calibrated images to produce well-calibrated posterior probabilities. We also note that using more training images will require the use of multi-GPU systems, which was beyond the scope of this work. Deep learning
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