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Detecting changes is of fundamental importance when analyzing data streamsand has many applications, e.g., predictive maintenance, fraud detection, ormedicine. A principled approach to detect changes is to compare thedistributions of observations within the stream to each other via hypothesistesting. Maximum mean discrepancy (MMD; also called energy distance) is awell-known (semi-)metric on the space of probability distributions. MMD givesrise to powerful non-parametric two-sample tests on kernel-enriched domainsunder mild conditions, which makes its deployment for change detectiondesirable. However, the classic MMD estimators suffer quadratic complexity,which prohibits their application in the online change detection setting. Wepropose a general-purpose change detection algorithm, Maximum Mean Discrepancyon Exponential Windows (MMDEW), which leverages the MMD two-sample test,facilitates its efficient online computation on any kernel-enriched domain, andis able to detect any disparity between distributions. Our experiments andanalysis show that (1) MMDEW achieves better detection quality thanstate-of-the-art competitors and that (2) the algorithm has polylogarithmicruntime and logarithmic memory requirements, which allow its deployment to thestreaming setting.

Maximum Mean Discrepancy on Exponential Windows for Online Change Detection