Geometric-Based Pruning Rules For Change Point Detection in Multiple Independent Time Series

TL;DR

This paper introduces geometric-based pruning rules for efficient change point detection in multiple independent time series, extending functional pruning methods to multivariate cases and demonstrating improved computational performance in simulations.

Contribution

It extends functional pruning techniques using geometric shapes to multivariate time series, enhancing efficiency in change point detection algorithms.

Findings

Geometric pruning rules outperform inequality-based methods in small-dimensional cases.

Proposed methods are efficient when the number of changes is small relative to data length.

Extensions can be applied to exponential family distributions.

Abstract

We consider the problem of detecting multiple changes in multiple independent time series. The search for the best segmentation can be expressed as a minimization problem over a given cost function. We focus on dynamic programming algorithms that solve this problem exactly. When the number of changes is proportional to data length, an inequality-based pruning rule encoded in the PELT algorithm leads to a linear time complexity. Another type of pruning, called functional pruning, gives a close-to-linear time complexity whatever the number of changes, but only for the analysis of univariate time series. We propose a few extensions of functional pruning for multiple independent time series based on the use of simple geometric shapes (balls and hyperrectangles). We focus on the Gaussian case, but some of our rules can be easily extended to the exponential family. In a simulation study we compare the computational efficiency of different geometric-based pruning rules. We show that for small dimensions (2, 3, 4) some of them ran significantly faster than inequality-based approaches in particular when the underlying number of changes is small compared to the data length.