  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.
