High Probability Latency Sequential Change Detection over an Unknown Finite Horizon

TL;DR

This paper addresses a finite horizon quickest change detection problem with unknown horizon, proposing a logarithmically increasing threshold CuSum test that is asymptotically optimal under false alarm constraints.

Contribution

It introduces a novel CuSum-based test with a logarithmically increasing threshold for unknown finite horizons, and derives an information-theoretic lower bound for latency.

Findings

Proposed test achieves asymptotic optimality in the finite horizon setting.

Derived lower bounds on minimum latency under false alarm constraints.

Experimental results demonstrate the effectiveness of the proposed method.

Abstract

A finite horizon variant of the quickest change detection problem is studied, in which the goal is to minimize a delay threshold (latency), under constraints on the probability of false alarm and the probability that the latency is exceeded. In addition, the horizon is not known to the change detector. A variant of the cumulative sum (CuSum) test with a threshold that increasing logarithmically with time is proposed as a candidate solution to the problem. An information-theoretic lower bound on the minimum value of the latency under the constraints is then developed. This lower bound is used to establish certain asymptotic optimality properties of the proposed test in terms of the horizon and the false alarm probability. Some experimental results are given to illustrate the performance of the test.