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Shell Theory: A Statistical Model of Reality

28 May 2021IEEE Transactions on Pattern Analysis and Machine Intelligence 2021 5archive 2025-07-28

Wen-Yan Lin, Siying Liu, Changhao Ren, Ngai-Man Cheung, Hongdong Li, Yasuyuki Matsushita

The foundational assumption of machine learning is that the data under consideration is separable into classes; while intuitively reasonable, separability constraints have proven remarkably difficult to formulate mathematically. We believe this problem is rooted in the mismatch between existing statistical techniques and commonly encountered data; object representations are typically high dimensional but statistical techniques tend to treat high dimensions a degenerate case. To address this problem, we develop a dedicated statistical framework for machine learning in high dimensions. The framework derives from the observation that object relations form a natural hierarchy; this leads us to model objects as instances of a high dimensional, hierarchal generative processes. Using a distance based statistical technique, also developed in this paper, we show that in such generative processes, instances of each process in the hierarchy, are almost-always encapsulated by a distinctive-shell that excludes almost-all other instances. The result is shell theory, a statistical machine learning framework in which separability constraints (distinctive-shells) are formally derived from the assumed generative process.

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Tasks

Anomaly DetectionBIG-bench Machine LearningOne-class classifierUnsupervised Anomaly Detection with Specified Settings -- 0.1% anomalyUnsupervised Anomaly Detection with Specified Settings -- 1% anomalyUnsupervised Anomaly Detection with Specified Settings -- 10% anomalyUnsupervised Anomaly Detection with Specified Settings -- 20% anomalyUnsupervised Anomaly Detection with Specified Settings -- 30% anomalymodel

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Anomaly Detection ASSIRA Cat Vs Dog Shell-based Anomaly (supervisered) ROC AUC 99.9 #1 of 1 Archive leaderboard report
Anomaly Detection Fashion-MNIST Shell-based Anomaly (supervised) ROC AUC 92.1 #8 of 12 Archive leaderboard report
Anomaly Detection STL-10 Shell-based Anomaly (supervised) ROC AUC 99.2 #1 of 1 Archive leaderboard report
Unsupervised Anomaly Detection with Specified Settings -- 0.1% anomaly CIFAR-10 Shell-Renormalized AUC-ROC 0.740 #5 of 6 Archive leaderboard report
Unsupervised Anomaly Detection with Specified Settings -- 0.1% anomaly Cats and Dogs Shell-Renormalized AUC-ROC 0.866 #3 of 6 Archive leaderboard report
Unsupervised Anomaly Detection with Specified Settings -- 0.1% anomaly STL-10 Shell-Renormalized AUC-ROC 0.803 #4 of 6 Archive leaderboard report
Unsupervised Anomaly Detection with Specified Settings -- 1% anomaly CIFAR-10 Shell-Renormalized AUC-ROC 0.756 #5 of 6 Archive leaderboard report
Unsupervised Anomaly Detection with Specified Settings -- 1% anomaly STL-10 Shell-Renormalized AUC-ROC 0.829 #5 of 6 Archive leaderboard report
Unsupervised Anomaly Detection with Specified Settings -- 10% anomaly CIFAR-10 Shell-Renormalized AUC-ROC 0.895 #2 of 6 Archive leaderboard report
Unsupervised Anomaly Detection with Specified Settings -- 10% anomaly Cats and Dogs Shell-Renormalized AUC-ROC 0.996 #1 of 6 Archive leaderboard report
Unsupervised Anomaly Detection with Specified Settings -- 10% anomaly STL-10 Shell-Renormalized AUC-ROC 0.997 #1 of 6 Archive leaderboard report
Unsupervised Anomaly Detection with Specified Settings -- 20% anomaly Cats and Dogs Shell-Renormalized AUC-ROC 0.953 #1 of 6 Archive leaderboard report
Unsupervised Anomaly Detection with Specified Settings -- 20% anomaly STL-10 Shell-Renormalized AUC-ROC 0.999 #1 of 6 Archive leaderboard report
Unsupervised Anomaly Detection with Specified Settings -- 20% anomaly cifar10 Shell-Renormalized AUC-ROC 0.896 #1 of 6 Archive leaderboard report
Unsupervised Anomaly Detection with Specified Settings -- 30% anomaly ASSIRA Cat Vs Dog Shell-Renormalized AUC-ROC 0.617 #6 of 6 Archive leaderboard report
Unsupervised Anomaly Detection with Specified Settings -- 30% anomaly CIFAR-10 Shell-Renormalized AUC-ROC 0.894 #1 of 6 Archive leaderboard report
Unsupervised Anomaly Detection with Specified Settings -- 30% anomaly STL-10 Shell-Renormalized AUC-ROC 0.999 #1 of 6 Archive leaderboard report

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