2019/12/25 by Tze Siong Lau, Wee Peng Tay, Lau, Tze Siong +1
Environmental Science · Mathematics · #FOS: Mathematics #Health, Environment, Cognitive Aging #Optimization and Control (math.OC) #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1912.11693
openalex publication_date 2019/12/25 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We consider the problem of quickest change detection (QCD) in a signal where\nits observations are obtained using a set of actions, and switching from one\naction to another comes with a cost. The objective is to design a stopping rule\nconsisting of a sampling policy to determine the sequence of actions used to\nobserve the signal and a stopping time to quickly detect for the change,\nsubject to a constraint on the average observation-switching cost. We propose\nan open-loop sampling policy of finite window size and a generalized likelihood\nratio (GLR) Cumulative Sum (CuSum) stopping time for the QCD problem. We show\nthat the GLR CuSum stopping time is asymptotically optimal with a properly\ndesigned sampling policy and formulate the design of this sampling policy as a\nquadratic programming problem. We prove that it is sufficient to consider\npolicies of window size not more than one when designing policies of finite\nwindow size and propose several algorithms that solve this optimization problem\nwith theoretical guarantees. For observation-dependent policies, we propose a\n2-threshold stopping time and an observation-dependent sampling policy. We\npresent a method to design the observation-dependent sampling policy based on\nopen-loop sampling policies. Finally, we apply our approach to the problem of\nQCD of a partially observed graph signal and empirically demonstrate the\nperformance of our proposed stopping times.\n