235 research outputs found
Data-Efficient Minimax Quickest Change Detection with Composite Post-Change Distribution
The problem of quickest change detection is studied, where there is an
additional constraint on the cost of observations used before the change point
and where the post-change distribution is composite. Minimax formulations are
proposed for this problem. It is assumed that the post-change family of
distributions has a member which is least favorable in some sense. An algorithm
is proposed in which on-off observation control is employed using the least
favorable distribution, and a generalized likelihood ratio based approach is
used for change detection. Under the additional condition that either the
post-change family of distributions is finite, or both the pre- and post-change
distributions belong to a one parameter exponential family, it is shown that
the proposed algorithm is asymptotically optimal, uniformly for all possible
post-change distributions.Comment: Submitted to IEEE Transactions on Info. Theory, Oct 2014. Preliminary
version presented at ISIT 2014 at Honolulu, Hawai
Quickest Change Detection of a Markov Process Across a Sensor Array
Recent attention in quickest change detection in the multi-sensor setting has
been on the case where the densities of the observations change at the same
instant at all the sensors due to the disruption. In this work, a more general
scenario is considered where the change propagates across the sensors, and its
propagation can be modeled as a Markov process. A centralized, Bayesian version
of this problem, with a fusion center that has perfect information about the
observations and a priori knowledge of the statistics of the change process, is
considered. The problem of minimizing the average detection delay subject to
false alarm constraints is formulated as a partially observable Markov decision
process (POMDP). Insights into the structure of the optimal stopping rule are
presented. In the limiting case of rare disruptions, we show that the structure
of the optimal test reduces to thresholding the a posteriori probability of the
hypothesis that no change has happened. We establish the asymptotic optimality
(in the vanishing false alarm probability regime) of this threshold test under
a certain condition on the Kullback-Leibler (K-L) divergence between the post-
and the pre-change densities. In the special case of near-instantaneous change
propagation across the sensors, this condition reduces to the mild condition
that the K-L divergence be positive. Numerical studies show that this low
complexity threshold test results in a substantial improvement in performance
over naive tests such as a single-sensor test or a test that wrongly assumes
that the change propagates instantaneously.Comment: 40 pages, 5 figures, Submitted to IEEE Trans. Inform. Theor
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