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...
| Publié dans: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 44(2022), 10 vom: 02. Okt., Seite 6438-6453 |
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| Auteur principal: | |
| Autres auteurs: | , , , , |
| Format: | Article en ligne |
| Langue: | English |
| Publié: |
2022
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| Accès à la collection: | IEEE transactions on pattern analysis and machine intelligence |
| Sujets: | Journal Article |
| Résumé: | 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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| Description: | Date Revised 15.09.2022 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
| ISSN: | 1939-3539 |
| DOI: | 10.1109/TPAMI.2021.3084598 |