TY - GEN
T1 - Quickest change detection and Kullback-Leibler divergence for two-state hidden Markov models
AU - Fuh, Cheng Der
AU - Mei, Yajun
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/9/28
Y1 - 2015/9/28
N2 - The quickest change detection problem is studied in two-state hidden Markov models (HMM), where the vector parameter θ of the HMM may change from θ0 to θ1 at some unknown time, and one wants to detect the true change as quickly as possible while controlling the false alarm rate. It turns out that the generalized likelihood ratio (GLR) scheme, while theoretically straightforward, is generally computationally infeasible for the HMM. To develop efficient but computationally simple schemes for the HMM, we first show that the recursive CUSUM scheme proposed in Fuh (Ann. Statist., 2003) can be regarded as a quasi-GLR scheme for some suitable pseudo post-change hypotheses. Next, we extend the quasi-GLR idea to propose recursive score schemes in a more complicated scenario when the post-change parameter θ1 of the HMM involves a real-valued nuisance parameter. Finally, our research provides an alternative approach that can numerically compute the Kullback-Leibler (KL) divergence of two-state HMMs via the invariant probability measure and the Fredholm integral equation.
AB - The quickest change detection problem is studied in two-state hidden Markov models (HMM), where the vector parameter θ of the HMM may change from θ0 to θ1 at some unknown time, and one wants to detect the true change as quickly as possible while controlling the false alarm rate. It turns out that the generalized likelihood ratio (GLR) scheme, while theoretically straightforward, is generally computationally infeasible for the HMM. To develop efficient but computationally simple schemes for the HMM, we first show that the recursive CUSUM scheme proposed in Fuh (Ann. Statist., 2003) can be regarded as a quasi-GLR scheme for some suitable pseudo post-change hypotheses. Next, we extend the quasi-GLR idea to propose recursive score schemes in a more complicated scenario when the post-change parameter θ1 of the HMM involves a real-valued nuisance parameter. Finally, our research provides an alternative approach that can numerically compute the Kullback-Leibler (KL) divergence of two-state HMMs via the invariant probability measure and the Fredholm integral equation.
KW - Change-point
KW - Hidden Markov model
KW - Kullback-Leibler divergence
KW - score test
KW - sequential detection
UR - http://www.scopus.com/inward/record.url?scp=84969808350&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84969808350&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2015.7282433
DO - 10.1109/ISIT.2015.7282433
M3 - Conference contribution
AN - SCOPUS:84969808350
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 141
EP - 145
BT - Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - IEEE International Symposium on Information Theory, ISIT 2015
Y2 - 14 June 2015 through 19 June 2015
ER -