Accurate Evaluation of Quickest Changepoint Detectors via Non-parametric Survival Analysis

Taiki Miyagawa, Akinori F. Ebihara

Keywords: Quickest changepoint detection, Change point detection, Average run length, Average detection delay, Estimation bias, Survival analysis

TL;DR: We propose non-parametric estimators for ARL and ADD in QCD under irregular sequence lengths by adapting the Kaplan-Meier estimator. We derive bias bounds and demonstrate reduced bias. Code will be released upon acceptance.

Abstract:

We propose non-parametric estimators for the average run length (ARL) and average detection delay (ADD) in quickest changepoint detection (QCD) under finite and irregular sequence lengths.
Although ARL and ADD are widely used as optimality criteria in theoretical and simulation studies, their application to real-world datasets is hindered by limited and irregular sequence lengths.
To address this issue, we propose non-parametric estimators for the ARL and ADD, termed *KM-ARL* and *KM-ADD*, by drawing an analogy between QCD and survival analysis to model detection probabilities under sequence truncation.
We derive estimation bias bounds and prove that they are asymptotically unbiased unless extrapolation is required.
Experiments on simulated and real-world datasets demonstrate their practical utility, enhancing robustness against limited and irregular sequence lengths, improving interpretability, and facilitating empirical, intuitive model selection.
Our Python code are provided in the supplementary material and will be released upon acceptance, offering ready-to-use implementations for practitioners.

Primary Area: learning on time series and dynamical systems

Submission Number: 6802