HMM conditional-likelihood based change detection with strict delay tolerance

Hidden Markov models (HMMs) have been widely used for anomaly and change point detection due to their representation power computational efficiency in capturing statistical dependencies time series. However, often information is integrated over relatively long observation windows, with detections made when the observed sequence’s likelihood under (null) HMM deviates significantly from its typical range. Three related limitations are: i) use of windows entails large decision delay, which may e.g. fail prevent machine failure/damage; ii) approaches do not narrowly identify an interval within occurred. Such could be useful process control, where one wants know how it takes control inputs induce desired points; iii) The statistic usually data current window, without consideration past observations. This suboptimal – this should conditioned on observations optimally account dependency In paper, we propose a framework overcomes all these limitations: applies standard Forward recursion, but evaluate subsequence subsequence’s entire past. approach efficiently conditional likelihoods intervals fixed length (hence d), until first detected. Here d design parameter whose proper value (needed quick response/mitigate damage) known given application domain; algorithm estimates detected lies; novel performance criterion well-matched low-delay, localized true rate (TDIR) also false positive (FPR) bias variance estimated point, as function d. proposed method shown outperform CUSUM algorithm, symbolic series analysis (STSA) methods, (evaluating unconditioned likelihood) instability onset combustion systems fatigue failure initiation material.