A Binning Approach to Quickest Change Detection with Unknown Post-Change Distribution

TL;DR

This paper introduces a binning-based sequential change detection method that efficiently detects distribution changes with unknown post-change distributions, balancing detection delay and false alarms.

Contribution

It proposes a novel binning approach with a recursive test statistic for quick change detection under unknown post-change distributions.

Findings

The method is computationally efficient due to recursive updates.

It achieves performance comparable or superior to existing non-parametric methods.

The approach effectively balances detection delay and false alarm rates.

Abstract

The problem of quickest detection of a change in distribution is considered under the assumption that the pre-change distribution is known, and the post-change distribution is only known to belong to a family of distributions distinguishable from a discretized version of the pre-change distribution. A sequential change detection procedure is proposed that partitions the sample space into a finite number of bins, and monitors the number of samples falling into each of these bins to detect the change. A test statistic that approximates the generalized likelihood ratio test is developed. It is shown that the proposed test statistic can be efficiently computed using a recursive update scheme, and a procedure for choosing the number of bins in the scheme is provided. Various asymptotic properties of the test statistic are derived to offer insights into its performance trade-off between average detection delay and average run length to a false alarm. Testing on synthetic and real data demonstrates that our approach is comparable or better in performance to existing non-parametric change detection methods.