Sequential Change-Point Detection via Online Convex Optimization
AbstractSequential 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
Share & Cite This Article
Cao, Y.; Xie, L.; Xie, Y.; Xu, H. Sequential Change-Point Detection via Online Convex Optimization. Entropy 2018, 20, 108.
Cao Y, Xie L, Xie Y, Xu H. Sequential Change-Point Detection via Online Convex Optimization. Entropy. 2018; 20(2):108.Chicago/Turabian Style
Cao, Yang; Xie, Liyan; Xie, Yao; Xu, Huan. 2018. "Sequential Change-Point Detection via Online Convex Optimization." Entropy 20, no. 2: 108.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.