[Paper Review] Bayesian Methods for Multiple Change-Point Detection with Reduced Communication

Eyal Nitzan, Topi Halme+1 more|arXiv (Cornell University)|Mar 24, 2020

Advanced Statistical Process Monitoring52 references15 citations

TL;DR

This paper proposes two Bayesian sequential change-point detection procedures—S-MAP and IS-MAP—for large-scale sensor networks with communication constraints. By monitoring only the sensors with the highest posterior probabilities of change points, the methods minimize detection delay while controlling the false discovery rate (FDR) under a specified threshold. The key contribution is analytical proof that both procedures maintain FDR control and achieve scalable average detection delay (ADD) that does not grow with the number of sensors, even under limited communication resources.

ABSTRACT

In many modern applications, large-scale sensor networks are used to perform statistical inference tasks. In this paper, we propose Bayesian methods for multiple change-point detection using a sensor network in which a fusion center (FC) can receive a data stream from each sensor. Due to communication limitations, the FC monitors only a subset of the sensors at each time slot. Since the number of change points can be high, we adopt the false discovery rate (FDR) criterion for controlling the rate of false alarms, while minimizing the average detection delay (ADD). We propose two Bayesian detection procedures that handle the communication limitations by monitoring the subset of the sensors with the highest posterior probabilities of change points having occurred. This monitoring policy aims to minimize the delay between the occurrence of each change point and its declaration using the corresponding posterior probabilities. One of the proposed procedures is more conservative than the second one in terms of having lower FDR at the expense of higher ADD. It is analytically shown that both procedures control the FDR under a specified tolerated level and are also scalable in the sense that they attain an ADD that does not increase asymptotically with the number of sensors. In addition, it is demonstrated that the proposed detection procedures are useful for trading off between reduced ADD and reduced average number of observations drawn until discovery. Numerical simulations are conducted for validating the analytical results and for demonstrating the properties of the proposed procedures.

Motivation & Objective

• To address the challenge of multiple change-point detection in large-scale sensor networks where communication bandwidth limits the number of sensors monitored at each time slot.
• To develop Bayesian detection procedures that minimize average detection delay (ADD) while strictly controlling the false discovery rate (FDR) under communication constraints.
• To ensure scalability by proving that the ADD of the proposed methods does not increase asymptotically with the number of sensors.
• To investigate the tradeoff between reducing detection delay and minimizing the average number of observations (ANO) drawn until detection.

Proposed method

• The S-MAP procedure selects, at each time slot, the subset of sensors with the highest posterior probabilities of change points, based on Bayesian updating of change-point beliefs.
• The IS-MAP procedure improves on S-MAP by using a lower detection threshold, reducing ADD at the cost of slightly higher FDR, while still maintaining FDR control.
• Both methods use sequential posterior probability updates and apply a stopping rule based on thresholding the posterior probability of change point occurrence.
• FDR control is analytically proven using the law of total expectation and bounding the expected proportion of false discoveries via conditional probabilities.
• Asymptotic ADD analysis is conducted under a geometric prior on change points, deriving lower and upper bounds that are independent of the number of sensors.
• The procedures are evaluated via simulations to validate theoretical findings and explore the tradeoff between ADD and ANO (average number of observations).

Experimental results

Research questions

• RQ1 Can Bayesian change-point detection be made scalable in large sensor networks with limited communication, such that detection delay does not grow with the number of sensors?
• RQ2 How can the false discovery rate (FDR) be analytically controlled in a sequential Bayesian multiple change-point detection framework under communication constraints?
• RQ3 What is the tradeoff between minimizing average detection delay (ADD) and minimizing the average number of observations (ANO) when only a subset of sensors is monitored at each time slot?
• RQ4 Can a more aggressive detection procedure (IS-MAP) achieve lower ADD than a conservative one (S-MAP) while still maintaining FDR control?

Key findings

• Both S-MAP and IS-MAP procedures analytically control the FDR under a specified tolerance level α, even under communication constraints.
• The asymptotic average detection delay (ADD) of both procedures remains bounded and does not increase with the number of sensors, proving scalability.
• The IS-MAP procedure achieves a lower ADD than S-MAP by using a lower detection threshold, with a quantitatively characterized improvement in asymptotic ADD.
• Simulations confirm that observing only a small proportion of sensors (e.g., q = 0.3) significantly reduces the average number of observations (ANO) while maintaining low ADD.
• The optimal tradeoff between ADD and ANO is achieved at a small observation proportion q ≪ 1, not at q = 1, demonstrating the benefit of selective monitoring.
• Theoretical analysis shows that the ADD upper bound for IS-MAP is tighter than for S-MAP, and both are independent of the sensor index k, confirming uniform performance across streams.