Meta-Learning for Anomaly Classification with Set Equivariant Networks: Application in the Milky Way

We present a new meta-learning approach for supervised anomaly classification / one-class classification using set equivariant networks. We focus our experiments on an astronomy application. Our problem setting is composed of a set of classification tasks. Each task has a (small) set of positive, labeled examples and a larger set of unlabeled examples. We expect the positive instances to be much more uncommon (i.e. 'anomalies') than the negative ones ('normal' class). We propose a novel use of equivariant networks for this setting. Specifically we use Deep Sets, which was developed for point-clouds and unordered sets and is equivariant to permutation. We propose to consider the set of positive examples of a given task as a 'point-cloud'. The key idea is that the network directly takes as input the set of positive examples in addition to the current example to classify. This allows the model to predict at test-time on new tasks using only positive labeled examples (i.e 'One-Class classification' setting) by design, potentially without retraining. However, the model is trained in a meta-learning regime on a dataset of several tasks with full-supervision (positive and negative labels). This setup is motivated by our target application on stellar streams. Streams are groups of stars sharing specific properties in various features. For a detected stream, we can determine a set of stars that likely belong to the stream. We aim to characterize the membership of all other nearby stars. We build a meta-dataset of simulated streams injected onto real data and evaluate on unseen synthetic streams and one known stream. Our experiments show encouraging results to explore furthermore equivariant networks for anomaly or 'one-class' classification in a meta-learning regime.