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Round Robin Active Sequential Change Detection for Dependent Multi-Channel Data

Anamitra Chaudhuri, Georgios Fellouris, Ali Tajer

TL;DR

This paper considers the problem of sequentially detecting a change in the joint distribution of multiple data sources under a sampling constraint, and a policy consists of a joint sampling and change-detection rule that achieves first-order asymptotic optimality.

Abstract

This paper considers the problem of sequentially detecting a change in the joint distribution of multiple data sources under a sampling constraint. Specifically, the channels or sources generate observations that are independent over time, but not necessarily independent at any given time instant. The sources follow an initial joint distribution, and at an unknown time instant, the joint distribution of an unknown subset of sources changes. Importantly, there is a hard constraint that only a fixed number of sources are allowed to be sampled at each time instant. The goal is to sequentially observe the sources according to the constraint, and stop sampling as quickly as possible after the change while controlling the false alarm rate below a user-specified level. The sources can be selected dynamically based on the already collected data, and thus, a policy for this problem consists of a joint sampling and change-detection rule. A non-randomized policy is studied, and an upper bound is established on its worst-case conditional expected detection delay with respect to both the change point and the observations from the affected sources before the change.

Round Robin Active Sequential Change Detection for Dependent Multi-Channel Data

TL;DR

This paper considers the problem of sequentially detecting a change in the joint distribution of multiple data sources under a sampling constraint, and a policy consists of a joint sampling and change-detection rule that achieves first-order asymptotic optimality.

Abstract

This paper considers the problem of sequentially detecting a change in the joint distribution of multiple data sources under a sampling constraint. Specifically, the channels or sources generate observations that are independent over time, but not necessarily independent at any given time instant. The sources follow an initial joint distribution, and at an unknown time instant, the joint distribution of an unknown subset of sources changes. Importantly, there is a hard constraint that only a fixed number of sources are allowed to be sampled at each time instant. The goal is to sequentially observe the sources according to the constraint, and stop sampling as quickly as possible after the change while controlling the false alarm rate below a user-specified level. The sources can be selected dynamically based on the already collected data, and thus, a policy for this problem consists of a joint sampling and change-detection rule. A non-randomized policy is studied, and an upper bound is established on its worst-case conditional expected detection delay with respect to both the change point and the observations from the affected sources before the change.
Paper Structure (37 sections, 31 theorems, 217 equations, 2 figures, 1 algorithm)

This paper contains 37 sections, 31 theorems, 217 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Multi-channel change-point model
  4. Sequential change detection with dynamic sampling control
  5. Change detection criteria
  6. Distributional assumptions
  7. Universal Asymptotic Lower Bound
  8. Round Robin Active Sequential Detection Policy
  9. Description of the policy
  10. Performance Analysis
  11. Asymptotic optimality
  12. A non-asymptotic upper bound
  13. Change in the Marginal Distributions of the Sources
  14. Change in Correlation
  15. Sampling two sources at a time ($m=2$)
  16. ...and 22 more sections

Key Result

Theorem 3.1

If eq:assm1 holds, then as $\gamma \to \infty$ we have

Figures (2)

  • Figure 1: Expected detection delay of the rules under the first study.
  • Figure 2: Expected detection delay of the rules under the second study (a) and third study (b).

Theorems & Definitions (38)

  • Theorem 3.1: Universal asymptotic lower bound
  • Theorem 4.1: False alarm control
  • Proposition 1
  • Corollary 4.1
  • Theorem 4.2: Asymptotic upper bound on detection delay
  • Theorem 4.3
  • Remark 4.1
  • Corollary 4.2
  • Proposition 2
  • Remark 4.2
  • ...and 28 more