The Characterization and Parallelization of Change Point Detection in Gaussian Distributed Time Series

Abstract

Change points, discrete jumps in measurements, are key to understanding the underlying dynamics of a system. Though many methods have been proposed for change point detection, there has been no explicit investigation into the limitations of these methods, specifically change point detection in Gaussian distributed time series that use log-likelihood ratio tests. This thesis characterizes Gaussian mean change point (GMCP) detection to probe the parameters of its effectiveness and limitations, and further extends the detection method to include changes in both the mean and variance, also known as Gaussian mean and variance change point (GMVCP) detection. Both GMCP and GMVCP detection were found to perform well even when there are subtle changes in the mean and/or variance and a high background-to-noise ratio and can, thus, be applied to many different kinds of chemical data that result in time series.

However, rapid advancements in technology have made the analysis of large amounts of data unfeasible due to time and memory constraints. This thesis implements parallel computing or processing, the simultaneous calculation or processing of segments of a dataset, on change point detection as a possible solution. The parallel algorithm proposed here includes a novel data segmentation scheme, and evalutes this algorithm by applying it to GMCP detection. Time decreased superlinearly with respect to the number of processes, and detection accuracy was minimally affected, suggesting that this parallelization algorithm is a valid method that addresses the problem of analyzing ”big data.”