Quickest Change Detection with Leave-one-out Density Estimation

TL;DR

This paper introduces a novel leave-one-out density estimation based CuSum test for quickest change detection that operates without prior knowledge of the post-change distribution and achieves asymptotic optimality.

Contribution

It develops a new window-limited LOO-CuSum test that does not require post-change training data and proves its asymptotic optimality under certain conditions.

Findings

LOO-CuSum test is asymptotically optimal as false alarm rate approaches zero.

Numerical results demonstrate the effectiveness of the proposed method compared to baseline tests.

The method does not rely on any knowledge of the post-change distribution.

Abstract

The problem of quickest change detection in a sequence of independent observations is considered. The pre-change distribution is assumed to be known, while the post-change distribution is completely unknown. A window-limited leave-one-out (LOO) CuSum test is developed, which does not assume any knowledge of the post-change distribution, and does not require any post-change training samples. It is shown that, with certain convergence conditions on the density estimator, the LOO-CuSum test is first-order asymptotically optimal, as the false alarm rate goes to zero. The analysis is validated through numerical results, where the LOO-CuSum test is compared with baseline tests that have distributional knowledge.