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Entropy 2018, 20(2), 108;

Sequential Change-Point Detection via Online Convex Optimization

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
Author to whom correspondence should be addressed.
Received: 1 September 2017 / Revised: 2 December 2017 / Accepted: 5 February 2018 / Published: 7 February 2018
(This article belongs to the Special Issue Information Theory in Machine Learning and Data Science)
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Sequential change-point detection when the distribution parameters are unknown is a fundamental problem in statistics and machine learning. When the post-change parameters are unknown, we consider a set of detection procedures based on sequential likelihood ratios with non-anticipating estimators constructed using online convex optimization algorithms such as online mirror descent, which provides a more versatile approach to tackling complex situations where recursive maximum likelihood estimators cannot be found. When the underlying distributions belong to a exponential family and the estimators satisfy the logarithm regret property, we show that this approach is nearly second-order asymptotically optimal. This means that the upper bound for the false alarm rate of the algorithm (measured by the average-run-length) meets the lower bound asymptotically up to a log-log factor when the threshold tends to infinity. Our proof is achieved by making a connection between sequential change-point and online convex optimization and leveraging the logarithmic regret bound property of online mirror descent algorithm. Numerical and real data examples validate our theory. View Full-Text
Keywords: sequential methods; change-point detection; online algorithms sequential methods; change-point detection; online algorithms

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Cao, Y.; Xie, L.; Xie, Y.; Xu, H. Sequential Change-Point Detection via Online Convex Optimization. Entropy 2018, 20, 108.

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