Algebraic Geometry and Statistical Theory
Algebraic Geometry and Statistical Theory
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代数几何与统计理论
DOI：
10.11540/bjsiam.31.3_7
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
渡辺澄夫
中科院分区：
文献类型：
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作者：
Rage Uday Kiran;Philippe Fournier-Viger;Jose Maria Luna;Jerry Chun-Wei Lin; Anirban Mondal;Sumio Watanabe;Sumio Watanabe;Sumio Watanabe;渡辺澄夫
许多统计模型和学习机不是正则的而是奇异的，因此传统的渐近正态性理论不能用于分析这类模型。本文阐述了新的数学理论，使我们能够澄清的渐近行为的推广损失和自由能基于代数几何。同时也介绍了这一理论如何应用于真实的世界问题的简短历史。
Many statistical models and learning machines are not regular but singular, hence the conventional theory using asymptotic normality can not be employed in analysis of such models. This paper explains the new mathematical theory which enables us to clarify the asymptotic behaviors of the generalization loss and the free energy based on algebraic geometry. Also the short history how this theory has been applied to real world problems is introduced.