Shell Theory: A Statistical Model of Reality

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 stat...

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Vydáno v:	IEEE Transactions on Pattern Analysis and Machine Intelligence Ročník 44; číslo 10; s. 6438 - 6453
Hlavní autoři:	Lin, Wen-Yan, Liu, Siying, Ren, Changhao, Cheung, Ngai-Man, Li, Hongdong, Matsushita, Yasuyuki
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York IEEE 01.10.2022 Institute of Electrical and Electronics Engineers (IEEE) The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	anomaly detection Artificial Intelligence and Robotics generative models hierarchical models High dimension incremental learning life-long learning Machine learning Machine learning algorithms Manifolds Mathematical model one-class learning Prediction algorithms Random variables semantic manifold Semantics Shell theory Statistical methods Statistical models statistics
ISSN:	0162-8828, 1939-3539, 1939-3539, 2160-9292
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Popis
Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23
ISSN:	0162-8828 1939-3539 1939-3539 2160-9292
DOI:	10.1109/TPAMI.2021.3084598