Abstract
We propose two fast algorithms for abrupt change detection in streaming data that can operate on arbitrary unknown data distributions before and after the change. The first algorithm, \(\textsf{MB-GT}\) , computes efficiently the average Euclidean distance between all pairs of data points before and after the hypothesized change. The second algorithm, \(\textsf{MB-CUSUM}\) , computes the log-likelihood ratio statistic for the data distributions before and after the change, similarly to the classical CUSUM algorithm, but unlike that algorithm, \(\textsf{MB-CUSUM}\) does not need to know the exact distributions, and uses kernel density estimates instead. Although a straightforward computation of the two change statistics would have computational complexity of O(N 4) with respect to the size N of the streaming data buffer, the proposed algorithms are able to use the computational structure of these statistics to achieve a computational complexity of only O(N 2) and memory requirement of O(N). Furthermore, the algorithms perform surprisingly well on dependent observations generated by underlying dynamical systems, unlike traditional change detection algorithms.
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Editor: Weng-Keen Wong.
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Nikovski, D., Jain, A. Fast adaptive algorithms for abrupt change detection. Mach Learn 79, 283–306 (2010). https://doi.org/10.1007/s10994-009-5122-x
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DOI: https://doi.org/10.1007/s10994-009-5122-x