Explaining outliers and anomalous groups via subspace density contrastive loss

Explainable AI refers to techniques by which the reasons underlying decisions taken by intelligent artifacts are single out and provided to users. Outlier detection is the task of individuating anomalous objects within a given data population they belong to. In this paper we propose a new technique to explain why a given data object has been singled out as anomalous. The explanation our technique returns also includes counterfactuals, each of which denotes a possible way to “repair” the outlier to make it an inlier. Thus, given in input a reference data population and an object deemed to be anomalous, the aim is to provide possible explanations for the anomaly of the input object, where an explanation consists of a subset of the features, called choice, and an associated set of changes to be applied, called mask, in order to make the object “behave normally”. The paper presents a deep learning architecture exploiting a features choice module and mask generation module in order to learn both components of explanations. The learning procedure is guided by an ad-hoc loss function that simultaneously maximizes (minimizes, resp.) the isolation of the input outlier before applying the mask (resp., after the application of the mask returned by the mask generation module) within the subspace singled out by the features choice module, all that while also minimizing the number of features involved in the selected choice. We consider also the case in which a common explanation is required for a group of outliers provided together in input. We present experiments on both artificial and real data sets and a comparison with competitors validating the effectiveness of the proposed approach.