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Change-Point Detection in Time-Series Data by Relative Density-Ratio Estimation (1203.0453v2)

Published 2 Mar 2012 in stat.ML, cs.LG, and stat.ME

Abstract: The objective of change-point detection is to discover abrupt property changes lying behind time-series data. In this paper, we present a novel statistical change-point detection algorithm based on non-parametric divergence estimation between time-series samples from two retrospective segments. Our method uses the relative Pearson divergence as a divergence measure, and it is accurately and efficiently estimated by a method of direct density-ratio estimation. Through experiments on artificial and real-world datasets including human-activity sensing, speech, and Twitter messages, we demonstrate the usefulness of the proposed method.

Citations (436)

Summary

  • The paper introduces a novel method that uses relative density-ratio estimation to accurately identify abrupt changes in time-series data.
  • It adapts uLSIF to the change-point detection problem and further enhances it with RuLSIF, offering robust performance without explicit density estimation.
  • Experimental evaluations on synthetic and real-world datasets demonstrate that the proposed approach outperforms traditional methods in both accuracy and stability.

Analysis of Change-Point Detection via Relative Density-Ratio Estimation

The paper introduces a novel approach to change-point detection in time-series data by leveraging relative density-ratio estimation techniques. The objective is to identify abrupt changes in the underlying properties of time-series data segments using non-parametric divergence measures. The authors employ the relative Pearson divergence, which is estimated efficiently through direct density-ratio methods, proving more robust and accurate compared to traditional parametric approaches.

Overview of Key Contributions

  1. Methodological Innovation: The paper presents two main improvements in the domain of non-parametric change-point detection. Firstly, it adapts the unconstrained least-squares importance fitting (uLSIF) to the change-point detection problem, utilizing a density-ratio approach that circumvents the challenges of explicit density estimation. Secondly, it evaluates the enhanced version relative uLSIF (RuLSIF), which accounts for potential unboundedness in density ratios, thereby improving the estimation reliability.
  2. Practical Application: The framework shows efficacy in a variety of datasets, including artificial constructs and real-world scenarios such as human-activity sensing and social media analysis, which demonstrates its versatility. The real-world application examples, particularly the Twitter dataset, provide insights into how change points align with actual events, validating the method’s practical relevance.
  3. Experimental Evaluation: Extensive experimental comparisons with established methods such as Singular Spectrum Transformation (SST), subspace methods, and one-class SVM illustrate the robustness and precision of the RuLSIF-based approach. Numerical results indicate superior performance metrics in terms of accuracy, attributing this success to effective handling of high-dimensionality challenges and leveraging a non-parametric estimation strategy.
  4. Robustness and Theoretical Guarantees: RuLSIF not only maintains the benefits of uLSIF, such as analytical solution derivation and numerical stability, but also addresses potential weaknesses in density-ratio estimation by using the concept of relative density ratios, thereby offering increased convergence properties.

Implications and Future Directions

The implications of utilizing direct density-ratio estimation for change-point detection are profound, particularly in fields requiring rapid adaptation to data distribution shifts such as finance, cyber-security, and environmental monitoring. By emphasizing non-parametric techniques, the method sidesteps assumptions about data distributions, making it adaptable to a wider range of data characteristics.

In future developments, heightened computational efficiency and the integration of dimensionality reduction techniques could further enhance the scalability of the method. Additionally, the application of this framework to real-time analytics in dynamic environments could expand its impact. The authors propose further exploration into hypothesis testing paradigms that could incorporate their techniques to produce actionable statistical thresholds.

Overall, the paper presents a significant contribution to the field of change-point detection by offering a method that balances robustness, adaptability, and computational efficiency, thereby setting a precedent for future research endeavors aimed at leveraging statistical learning in complex data environments.