Data-Driven Quickest Change Detection in Hidden Markov Models

The problem of quickest change detection in hidden Markov models (HMMs) is investigated. A sequence of samples are generated from a HMM, and at some unknown time, the transition kernel and/or the emission probability of the HMM changes. The goal is to detect the change as soon as possible subject to false alarm constraints. The data-driven setting is investigated, where none of the pre-, post-change Markov transition kernels or the emission probabilities are known. In this paper, a kernel based data-driven algorithm is developed. Performance bounds on its average running length (ARL) to false alarm and worst-case average detection delay (WADD) are theoretically characterized, where the WADD is at most of the order of the logarithm of the ARL. Numerical results are provided to validate the performance of the proposed algorithm.