Maximum Mean Discrepancy on Exponential Windows for Online Change Detection

TL;DR

This paper introduces MMDEW, an efficient online change detection method using MMD with exponential windows, offering fast computation and improved performance for data stream analysis.

Contribution

The paper proposes MMDEW, a novel change detection algorithm that combines MMD with exponential windows to achieve polylogarithmic runtime and logarithmic memory complexity.

Findings

Outperforms existing methods on benchmark data streams

Achieves polylogarithmic runtime and logarithmic memory usage

Effectively detects distribution changes in data streams

Abstract

Detecting changes is of fundamental importance when analyzing data streams and has many applications, e.g., in predictive maintenance, fraud detection, or medicine. A principled approach to detect changes is to compare the distributions of observations within the stream to each other via hypothesis testing. Maximum mean discrepancy (MMD), a (semi-)metric on the space of probability distributions, provides powerful non-parametric two-sample tests on kernel-enriched domains. In particular, MMD is able to detect any disparity between distributions under mild conditions. However, classical MMD estimators suffer from a quadratic runtime complexity, which renders their direct use for change detection in data streams impractical. In this article, we propose a new change detection algorithm, called Maximum Mean Discrepancy on Exponential Windows (MMDEW), that combines the benefits of MMD with an efficient computation based on exponential windows. We prove that MMDEW enjoys polylogarithmic runtime and logarithmic memory complexity and show empirically that it outperforms the state of the art on benchmark data streams.