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Titlebook: Geometric Structures of Statistical Physics, Information Geometry, and Learning; SPIGL‘20, Les Houche Frédéric Barbaresco,Frank Nielsen Con

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书目名称Geometric Structures of Statistical Physics, Information Geometry, and Learning
副标题SPIGL‘20, Les Houche
编辑Frédéric Barbaresco,Frank Nielsen
视频video
概述Provides new geometric foundations of inference in machine learning based on statistical physics.Deepens mathematical physics models with new insights from statistical machine learning.Combines numeri
丛书名称Springer Proceedings in Mathematics & Statistics
图书封面Titlebook: Geometric Structures of Statistical Physics, Information Geometry, and Learning; SPIGL‘20, Les Houche Frédéric Barbaresco,Frank Nielsen Con
描述.Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces..This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les
出版日期Conference proceedings 2021
关键词Conference Proceedings; Statistical inference; Geometric mechanics; Lie group machine learning; Informat
版次1
doihttps://doi.org/10.1007/978-3-030-77957-3
isbn_softcover978-3-030-77959-7
isbn_ebook978-3-030-77957-3Series ISSN 2194-1009 Series E-ISSN 2194-1017
issn_series 2194-1009
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
The information of publication is updating

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Sequelae of Ebola Virus Disease, by briefly reviewing the different approaches to build densities on a manifold and shows the interest of wrapped distributions. We then construct wrapped densities on .(.) and discuss their statistical estimation. We conclude by an opening to the case of symmetric spaces.
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https://doi.org/10.1007/978-94-015-5853-2nsion space. The entropy is generalized as a 4-vector and the temperature as a 5-vector. The introduction of the friction and momentum tensors allows to obtain a covariant formulation of the first and second principles of Thermodynamics.
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Galilean Thermodynamics of Continuansion space. The entropy is generalized as a 4-vector and the temperature as a 5-vector. The introduction of the friction and momentum tensors allows to obtain a covariant formulation of the first and second principles of Thermodynamics.
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Nonparametric Estimations and the Diffeological Fisher Metricnd slightly extending Lê’s theory in [.] to include weakly .-diffeological statistical models. Then we introduce the resulting notions of the diffeological Fisher distance, the diffeological Hausdorff–Jeffrey measure and explain their role in classical and Bayesian nonparametric estimation problems in statistics.
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