Optimal Online Change Detection via Random Fourier Features

TL;DR

This paper introduces a novel online change point detection method using random Fourier features that is efficient, does not require prior training data, and guarantees optimal detection delay.

Contribution

The paper presents a new online change detection algorithm based on kernel testing with random Fourier features, eliminating the need for training data and window parameters.

Findings

Algorithm runs with logarithmic time and space complexity.

Proven to have minimax optimal detection delay.

Performs competitively on real and synthetic data.

Abstract

This article studies the problem of online non-parametric change point detection in multivariate data streams. We approach the problem through the lens of kernel-based two-sample testing and introduce a sequential testing procedure based on random Fourier features, running with logarithmic time complexity per observation and with overall logarithmic space complexity. The algorithm has two advantages compared to the state of the art. First, our approach is genuinely online, and no access to training data known to be from the pre-change distribution is necessary. Second, the algorithm does not require the user to specify a window parameter over which local tests are to be calculated. We prove strong theoretical guarantees on the algorithm's performance, including information-theoretic bounds demonstrating that the detection delay is optimal in the minimax sense. Numerical studies on real and synthetic data show that our algorithm is competitive with respect to the state of the art.