Dynamic programming by exchangeability
SIAM Journal on Computing
Elements of information theory
Elements of information theory
Information Theory: Coding Theorems for Discrete Memoryless Systems
Information Theory: Coding Theorems for Discrete Memoryless Systems
Convex Optimization
On the zero-rate error exponent for a BSC with noisy feedback
Problems of Information Transmission
Information bounds and quick detection of parameter changes in stochastic systems
IEEE Transactions on Information Theory
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
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A novel quickest detection setting is proposed, generalizing the well-known Bayesian change-point detection model. Suppose {(Xi,Yi)}i≥1 is a sequence of pairs of random variables, and that S is a stopping time with respect to {Xi}i≥1. The problem is to find a stopping time T with respect to {Yi}i≥1 that optimally tracks S, in the sense that T minimizes the expected reaction delay E(T-S)+, while keeping the false-alarm probability P(T S) below a given threshold α ∈ [0,1]. This problem formulation applies in several areas, such as in communication, detection, forecasting, and quality control. Our results relate to the situation where the Xi's and Yi's take values in finite alphabets and where S is bounded by some positive integer κ. By using elementary methods based on the analysis of the tree structure of stopping times, we exhibit an algorithm that computes the optimal average reaction delays for all α ∈ [0,1], and constructs the associated optimal stopping times T. Under certain conditions on {(Xi,Yi)}i≥1 and S, the algorithm running time is polynomial in κ.