# Dimension-Calibrated Unexplained Mass: An Interpretable Drift Statistic for Contamination Monitoring in Data Streams

arXiv: https://arxiv.org/abs/2607.16811 · HTML: https://mlsanity.com/paper/2607.16811/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 58 references that are in the map.
- First posted on arXiv 18 Jul 2026.

## Builds on (most cited first, 17 of 17)

- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift](https://mlsanity.com/paper/1810.11953/) (2018)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [PyOD: A Python Toolbox for Scalable Outlier Detection](https://mlsanity.com/paper/1901.01588/) (2019)
- [ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions](https://mlsanity.com/paper/2201.00382/) (2022)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Learning Deep Kernels for Non-Parametric Two-Sample Tests](https://mlsanity.com/paper/2002.09116/) (2020)
- [MMD Aggregated Two-Sample Test](https://mlsanity.com/paper/2110.15073/) (2021)
- [Model Based Explanations of Concept Drift](https://mlsanity.com/paper/2303.09331/) (2023)
- [AutoML Two-Sample Test](https://mlsanity.com/paper/2206.08843/) (2022)
- [STUDD: A Student-Teacher Method for Unsupervised Concept Drift Detection](https://mlsanity.com/paper/2103.00903/) (2021)
- [Unsupervised Concept Drift Detection from Deep Learning Representations in Real-time](https://mlsanity.com/paper/2406.17813/) (2024)
- [Online Drift Detection with Maximum Concept Discrepancy](https://mlsanity.com/paper/2407.05375/) (2024)
- [Concept Drift Detection via Equal Intensity k-means Space Partitioning](https://mlsanity.com/paper/2004.11587/) (2020)
- [Change Detection for Local Explainability in Evolving Data Streams](https://mlsanity.com/paper/2209.02764/) (2022)
- [Nonparametric and Online Change Detection in Multivariate Datastreams using QuantTree](https://mlsanity.com/paper/2208.14801/) (2022)

## Abstract (arXiv)

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): each fitted component is 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. We identify why this statistic collapses in high dimension and repair it. Under a correct component a normal point in d dimensions lies about sqrt(d) sigma from the mean, so once d exceeds 9 essentially every point exceeds a fixed 3-sigma radius: window-level ROC-AUC is exactly 0.50 on Satellite (d=36) and Optdigits (d=64). Calibrating the radius to sqrt(chi-squared_d(0.99)) removes the collapse -- AUC 1.00 and 0.89 -- while leaving low dimensions unchanged. Across seven public benchmarks, five seeds, and eight model-free detectors spanning the kernel, classifier, projection, density-difference, transport, likelihood and partition families, the repaired statistic is best or tied-best on five of seven datasets at 10% window contamination (its two losses are Pendigits, where the whole field beats it, and Optdigits), and as contamination becomes sparse the sample-level detectors fade toward chance while it degrades most gracefully: at 2% its mean AUC across the benchmarks is 0.86 against at most 0.73 for any model-free detector (1.00 vs. MMD's 0.72 on KDD-http) -- while alone among them reporting which regime the data left and how far outside it the window lies. We delimit its scope honestly: unexplained mass detects and explains novel-regime drift but is blind by construction to in-support re-weighting of known regimes, where distribution-level tests are required and explain nothing; and the underlying density model's EVT-calibrated false-alarm rates degrade above d of about 36. All code and experiments are released.