Maximum Mean Discrepancy on Exponential Windows for Online Change Detection
This addresses the need for efficient change detection in applications like predictive maintenance and fraud detection, representing a novel method for a known bottleneck.
The paper tackles the problem of detecting changes in data streams using Maximum Mean Discrepancy (MMD), which has high computational costs, by proposing MMDEW, an algorithm that achieves polylogarithmic runtime and outperforms state-of-the-art methods on benchmarks.
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.