Dimension-Calibrated Unexplained Mass: An Interpretable GMM Drift Statistic that Matches Kernel Two-Sample Tests

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arXiv:2607.16811v3 Announce Type: replace Abstract: Drift detectors that work tend not to explain themselves, and drift detectors that explain themselves tend to fail in high dimension. We close that gap for Gaussian mixture models (GMMs). Fitting a GMM to normal data makes each component a named "regime," and the fraction of a stream window matching no regime -- its unexplained mass -- is a drift signal that is simultaneously its own explanation. This statistic degrades as dimension grows; we identify the mechanism and remove it. Under a correct component, a normal point in d dimensions sits at about sqrt(d) sigma from the mean, so the customary fixed 3-sigma radius admits every point once d exceeds about 9, and window-level ROC-AUC collapses to exactly 0.50 on Satellite (d=36) and Optdigits (d=64). Replacing the fixed radius with the dimension-calibrated chi-squared quantile removes the saturation entirely: AUC rises to 1.00 and 0.89 respectively, leaving low-dimensional cases unchanged. The resulting interpretable detector matches a model-free kernel two-sample test (MMD) at every dimension from 3 to 64, across seven public benchmarks and five random splits, while reporting which regime the data left and how far outside it the window lies. We delimit its scope: unexplained mass detects and explains novel-regime drift, but is blind by construction to in-support re-weighting of existing regimes, where MMD is required and supplies no explanation. Two GMM-to-GMM divergences serve as ablations, and the same density model is a competent point-anomaly detector on par with six …

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