Non-Parametric Methods Applied to the N-Sample Series Comparison

TL;DR

This paper surveys non-parametric methods for anomaly and similarity detection in multidimensional series, and introduces an effective NCDF technique for small-dimensional series with scalable extensions.

Contribution

It provides a comprehensive survey of current methods and proposes a new scalable NCDF approach for low-dimensional series comparison.

Findings

Survey of conformal prediction, kernels, and Kolmogorov measures

Introduction of a scalable NCDF method for small-dimensional series

Extensions that improve scalability with higher dimensionality

Abstract

Anomaly and similarity detection in multidimensional series have a long history and have found practical usage in many different fields such as medicine, networks, and finance. Anomaly detection is of great appeal for many different disciplines; for example, mathematicians searching for a unified mathematical formulation based on probability, statisticians searching for error bound estimates, and computer scientists who are trying to design fast algorithms, to name just a few. In summary, we have two contributions: First, we present a self-contained survey of the most promising methods being used in the fields of machine learning, statistics, and bio-informatics today. Included we present discussions about conformal prediction, kernels in the Hilbert space, Kolmogorov's information measure, and non-parametric cumulative distribution function comparison methods (NCDF). Second, building upon this foundation, we provide a powerful NCDF method for series with small dimensionality. Through a combination of data organization and statistical tests, we describe extensions that scale well with increased dimensionality.