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High Probability Latency Sequential Change Detection over an Unknown Finite Horizon

Yu-Han Huang, Venugopal V. Veeravalli

TL;DR

An information-theoretic lower bound on the minimum value of the latency under the constraints is developed and used to establish certain asymptotic optimality properties of the proposed test in terms of the horizon and the false alarm probability.

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.

High Probability Latency Sequential Change Detection over an Unknown Finite Horizon

TL;DR

An information-theoretic lower bound on the minimum value of the latency under the constraints is developed and used to establish certain asymptotic optimality properties of the proposed test in terms of the horizon and the false alarm probability.

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.
Paper Structure (10 sections, 8 theorems, 39 equations, 2 figures)

This paper contains 10 sections, 8 theorems, 39 equations, 2 figures.

Table of Contents

  1. Introduction
  2. High Probability Low Latency Quickest Change Detection
  3. Performance of CUSUM Detector
  4. Asymptotic Information-Theoretic Lower Bound on the High Probability Detection Delay
  5. Simulation
  6. Conclusion
  7. Proof of Lemma \ref{['lem:sup_martin']}
  8. Proof of Lemma \ref{['lem:LowBoundFA']}
  9. Proof of Lemma \ref{['lem:sub_martin']}
  10. Proof of Lemma \ref{['lem:d_inf']}

Key Result

Theorem 1

For any horizon $T\in\mathbb{N}$ and $r>1$,

Figures (2)

  • Figure 1: High probability latency $d_r$ as a function of the horizon $T$, with $\delta_{\mathrm{F}}=\delta_{\mathrm{D}} =0.01$.
  • Figure 2: High probability latency $d_{r}$ as a function of $\delta = \delta_{\mathrm{F}} = \delta_{\mathrm{D}}$, with the horizon $T=10000$

Theorems & Definitions (15)

  • Theorem 1: TVT-CuSum Test: False Alarm Probability
  • proof
  • Theorem 2: High Probability Latency for TVT-CuSum Test
  • proof
  • Theorem 3: Lower Bound for High Probability Latency
  • proof
  • Corollary 1
  • Lemma 1
  • proof
  • Lemma 2
  • ...and 5 more