Greedy Gaussian Segmentation of Multivariate Time Series

TL;DR

This paper introduces a scalable greedy algorithm for segmenting multivariate time series into Gaussian-distributed segments, enabling efficient analysis of large datasets with high-dimensional data.

Contribution

The paper presents GGS, a linear-time heuristic for Gaussian segmentation that guarantees local optimality and scales to high-dimensional, long time series.

Findings

GGS efficiently segments high-dimensional financial and text data.

The method scales linearly with time series length.

It provides a locally optimal segmentation solution.

Abstract

We consider the problem of breaking a multivariate (vector) time series into segments over which the data is well explained as independent samples from a Gaussian distribution. We formulate this as a covariance-regularized maximum likelihood problem, which can be reduced to a combinatorial optimization problem of searching over the possible breakpoints, or segment boundaries. This problem can be solved using dynamic programming, with complexity that grows with the square of the time series length. We propose a heuristic method that approximately solves the problem in linear time with respect to this length, and always yields a locally optimal choice, in the sense that no change of any one breakpoint improves the objective. Our method, which we call greedy Gaussian segmentation (GGS), easily scales to problems with vectors of dimension over 1000 and time series of arbitrary length. We discuss methods that can be used to validate such a model using data, and also to automatically choose appropriate values of the two hyperparameters in the method. Finally, we illustrate our GGS approach on financial time series and Wikipedia text data.