Quickest Detection of Bad Changes While Avoiding False Alarms for Confusing Changes

Core Concepts

The key goal is to detect a bad change as quickly as possible while avoiding raising false alarms for pre-change or confusing change distributions.

Abstract

This work studies a quickest change detection (QCD) problem where the change can be either a "bad change" that the system aims to detect quickly, or a "confusing change" that is not of interest. The authors identify specific scenarios where standard CuSum procedures fail to achieve the goal of detecting bad changes quickly while avoiding false alarms for confusing changes. To address this challenge, the authors propose two novel CuSum-based procedures, Successive CuSum (S-CuSum) and Joint CuSum (J-CuSum), that leverage two CuSum statistics. These procedures are shown to work across all possible combinations of pre-change, bad change, and confusing change distributions. The authors provide analytical performance guarantees for both S-CuSum and J-CuSum, proving that they fulfill the false alarm requirement and achieve near-optimal detection delay. The procedures are also computationally efficient as they only require simple recursive updates. Numerical results corroborate the theoretical findings and demonstrate the advantages of the proposed methods over standard single CuSum procedures.

Stats

The authors do not provide any specific numerical data or statistics in the content. The work focuses on the theoretical analysis and algorithmic design of the proposed detection procedures.

Quotes

"In the classical formulation of the QCD problem, the objective is to detect any change in the distribution. However, in many applications, there can be confusing changes that are not of primary interest, and raising an alarm for a confusing change may result in wasting human resources on checking the system." "Our QCD with confusing change problems differ from those problems as they still aim to raise an alarm as soon as any change happens, while we avoid raising an alarm if the change is a confusing change."

Key Insights Distilled From

Quickest Change Detection with Confusing Change

by Yu-Zhen Jani... at arxiv.org 05-03-2024

https://arxiv.org/pdf/2405.00842.pdf

Deeper Inquiries

What are some real-world applications where the proposed QCD with confusing change problem formulation would be particularly relevant

The proposed QCD with confusing change problem formulation could be particularly relevant in various real-world applications where distinguishing between different types of changes is crucial for decision-making or system control. Cybersecurity: In cybersecurity applications, where different types of network activities need to be monitored, quickly detecting malicious activities while avoiding false alarms for benign fluctuations is essential. Industrial Process Monitoring: In manufacturing or industrial process monitoring, being able to differentiate between normal variations, sensor errors, and actual process changes can help in maintaining quality control and efficiency. Healthcare: In healthcare settings, especially in patient monitoring systems, being able to detect significant changes in health parameters while filtering out minor fluctuations can aid in timely intervention and patient care. Environmental Monitoring: In environmental monitoring systems, distinguishing between natural variations, sensor errors, and actual environmental changes can help in accurate data analysis and decision-making. Financial Markets: In financial markets, detecting unusual trading patterns or anomalies while filtering out regular market fluctuations is crucial for risk management and fraud detection.

How could the proposed procedures be extended to handle scenarios with multiple types of confusing changes or changes with time-varying distributions

To handle scenarios with multiple types of confusing changes or changes with time-varying distributions, the proposed procedures could be extended in the following ways: Adaptive Thresholds: Implement adaptive thresholding techniques that adjust the detection thresholds based on the characteristics of the observed data. This can help in accommodating multiple types of changes with varying magnitudes. Dynamic Model Updating: Incorporate mechanisms for dynamically updating the underlying distribution models based on the observed data. This can help in adapting to changes in the distribution over time. Machine Learning Integration: Integrate machine learning algorithms that can learn and adapt to different types of changes in the data distribution. This can enhance the system's ability to detect and differentiate between various types of changes. Ensemble Methods: Explore ensemble methods that combine multiple detection algorithms to handle different types of changes effectively. By leveraging the strengths of different algorithms, the system can improve overall detection performance.

Are there any alternative algorithmic approaches, beyond the CuSum-based methods, that could be explored to tackle the QCD with confusing change problem

Beyond CuSum-based methods, alternative algorithmic approaches that could be explored to tackle the QCD with confusing change problem include: Machine Learning Techniques: Utilize machine learning algorithms such as neural networks, support vector machines, or random forests for change detection. These algorithms can learn complex patterns in the data and adapt to different types of changes. Bayesian Inference: Implement Bayesian inference methods to model the uncertainty in the data and make probabilistic decisions about changes. Bayesian approaches can handle multiple types of changes and provide a principled way to update beliefs over time. Reinforcement Learning: Explore reinforcement learning techniques to develop adaptive change detection policies. Reinforcement learning algorithms can learn optimal decision-making strategies in dynamic environments with changing distributions. Non-parametric Methods: Investigate non-parametric methods such as kernel density estimation or nearest neighbor approaches for change detection. These methods do not rely on specific distribution assumptions and can adapt to different types of changes in the data. By exploring these alternative approaches, researchers can enhance the robustness and flexibility of change detection systems in scenarios with confusing changes.