Transfer Neyman-Pearson Algorithm for Outlier Detection

We consider the problem of transfer learning in outlier detection where target abnormal data is rare. While transfer learning has been considered extensively in traditional balanced classification, the problem of transfer in outlier detection and more generally in imbalanced classification settings has received less attention. We propose a general meta-algorithm which is shown theoretically to yield strong guarantees w.r.t. to a range of changes in abnormal distribution, and at the same time amenable to practical implementation. We then investigate different instantiations of this general meta-algorithm, e.g., based on multi-layer neural networks, and show empirically that they outperform natural extensions of transfer methods for traditional balanced classification settings (which are the only solutions available at the moment).

Distribution-Free Rates in Neyman-Pearson Classification

We consider the problem of Neyman-Pearson classification which models unbalanced classification settings where error w.r.t. a distribution $\mu_1$ is to be minimized subject to low error w.r.t. a different distribution $\mu_0$. Given a fixed VC class $\mathcal{H}$ of classifiers to be minimized over, we provide a full characterization of possible distribution-free rates, i.e., minimax rates over the space of all pairs $(\mu_0, \mu_1)$. The rates involve a dichotomy between hard and easy classes $\mathcal{H}$ as characterized by a simple geometric condition, a three-points-separation condition, loosely related to VC dimension.

Tight Rates in Supervised Outlier Transfer Learning

A critical barrier to learning an accurate decision rule for outlier detection is the scarcity of outlier data. As such, practitioners often turn to the use of similar but imperfect outlier data from which they might transfer information to the target outlier detection task. Despite the recent empirical success of transfer learning approaches in outlier detection, a fundamental understanding of when and how knowledge can be transferred from a source to a target outlier detection task remains elusive. In this work, we adopt the traditional framework of Neyman-Pearson classification -- which formalizes supervised outlier detection -- with the added assumption that one has access to some related but imperfect outlier data. Our main results are as follows: We first determine the information-theoretic limits of the problem under a measure of discrepancy that extends some existing notions from traditional balanced classification; interestingly, unlike in balanced classification, seemingly very dissimilar sources can provide much information about a target, thus resulting in fast transfer. We then show that, in principle, these information-theoretic limits are achievable by adaptive procedures, i.e., procedures with no a priori information on the discrepancy between source and target outlier distributions.