Sparse Robust Regression for Explaining Classifiers.

Real-world datasets are often characterised by outliers, points far from the majority of the points, which might negatively influence modelling of the data. In data analysis it is hence important to use methods that are robust to outliers. In this paper we develop a robust regression method for finding the largest subset in the data that can be approximated using a sparse linear model to a given precision. We show that the problem is NP-hard and hard to approximate. We present an efficient algorithm, termed SLISE, to find solutions to the problem. Our method extends current state-of-the-art robust regression methods, especially in terms of scalability on large datasets. Furthermore, we show that our method can be used to yield interpretable explanations for individual decisions by opaque, black box, classifiers. Our approach solves shortcomings in other recent explanation methods by not requiring sampling of new data points and by being usable without modifications across various data domains. We demonstrate our method using both synthetic and real-world regression and classification problems.