Greedy Gaussian segmentation of multivariate time series

• Published in: Advances in data analysis and classification Vol. 13; no. 3; pp. 727 - 751
• Main Authors: Hallac, David, Nystrup, Peter, Boyd, Stephen
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2019; Springer Nature B.V
• Subjects: Chemistry and Earth Sciences; Combinatorial analysis; Computer Science; Covariance; Data Mining and Knowledge Discovery; Dynamic programming; Economics; Finance; Gaussian distribution; Health Sciences; Heuristic methods; Humanities; Insurance; Law; Management; Mathematics and Statistics; Medicine; Normal distribution; Physics; Regular Article; Segmentation; Statistical Theory and Methods; Statistics; Statistics for Business; Statistics for Engineering; Statistics for Life Sciences; Statistics for Social Sciences; Time series; Change-point detection; Greedy algorithms; Covariance regularization; Time series analysis; Financial regimes; 37M10: Time series analysis; Text segmentation
• ISSN: 1862-5347; 1862-5355
• DOI: 10.1007/s11634-018-0335-0

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.