Kernel-based Outlier Detection using the Inverse Christoffel Function
This work addresses outlier detection for security and various applications, offering a computationally efficient method that is incremental over prior work.
The authors tackled the computational intractability of outlier detection using the inverse Christoffel function for high-dimensional data by proposing a kernelized variant, achieving the best average AUPRC score, rank, and lowest root mean square deviation on 15 datasets.
Outlier detection methods have become increasingly relevant in recent years due to increased security concerns and because of its vast application to different fields. Recently, Pauwels and Lasserre (2016) noticed that the sublevel sets of the inverse Christoffel function accurately depict the shape of a cloud of data using a sum-of-squares polynomial and can be used to perform outlier detection. In this work, we propose a kernelized variant of the inverse Christoffel function that makes it computationally tractable for data sets with a large number of features. We compare our approach to current methods on 15 different data sets and achieve the best average area under the precision recall curve (AUPRC) score, the best average rank and the lowest root mean square deviation.