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Copula熵:理论和应用

Copula Entropy: Theory and Applications

摘要:统计独立性是统计学和机器学习领域的基础性概念,如何表示和度量统计独立性是该领域的基本问题。Copula理论提供了统计相关关系表示的理论工具,而Copula熵理论则给出了度量统计独立性的概念工具。本文综述了Copula熵的理论和应用,概述了其基本概念定义、定理和性质,以及估计方法。介绍了Copula熵研究的最新进展,包括其在统计学的六个基本问题(结构学习、关联发现、变量选择、因果发现、域自适应和正态性检验等)上的理论应用。讨论了前四个理论应用之间的关系,以及其对应的深层次的相关性和因果性概念之间的联系,并将Copula熵的(条件)独立性度量框架与基于核函数和距离相关的同类框架进行了对比。简述了Copula熵在理论物理学、理论化学、化学信息学、水文学、环境气象学、生态学、动物形态学、农学、认知神经学、运动神经学、计算神经学、心理学、系统生物学、生物信息学、临床诊断学、老年医学、精神病学、公共卫生学、经济学、社会学、教育学、法学、政治学,以及能源工程、土木工程、制造工程、可靠性工程、航空航天、通信工程、测绘工程和金融工程等领域的实际应用。

英文摘要:Statistical independence is the core concept in statistics and machine learning. Representing and measuring independence is of fundamental importance in the field. Copula theory provides the tool for representing statistical independence, and Copula Entropy (CE) presents the tool for measuring statistical independence. This paper survey the theory and applications of CE, including the basic definition, theorem, properties, and estimation method of CE. The theoretical applications of CE on structure learning, association discovery, variable selection, causal discovery, domain adaptation, and multivariate normality test are reviewed. The relationships between the former four applications and their connection to the concepts of correlation and causality are discussed. The three frameworks on measuring statistical independence and conditional independence based on CE, kernel method, and distance correlation are compared. The multidisciplinary applications of CE on theoretical physics, theoretical chemistry, cheminformatics, hydrology, meteorology, ecology, animal morphology, agronomy, cognitive neuroscience, motor neuroscience, computational neuroscience, psychology, system biology, bioinformatics, clinical diagnostics, geriatrics, psychiatry, public health, economics, sociology, pedagogy, law, political science, energy, civil engineering, manufacture, reliability, aeronautics and astronautics, communication, remote sensing, and finance are introduced.

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[V9] 2022-08-25 10:32:25 chinaXiv:202105.00070V9 下载全文
[V8] 2022-07-28 08:26:52 chinaXiv:202105.00070v8 查看此版本 下载全文
[V7] 2022-06-23 06:24:01 chinaXiv:202105.00070v7 查看此版本 下载全文
[V6] 2022-05-12 17:34:17 chinaXiv:202105.00070v6 查看此版本 下载全文
[V5] 2022-03-03 20:27:33 chinaXiv:202105.00070v5 查看此版本 下载全文
[V4] 2021-11-10 22:28:38 chinaXiv:202105.00070v4 查看此版本 下载全文
[V3] 2021-10-05 19:15:33 chinaXiv:202105.00070v3 查看此版本 下载全文
[V2] 2021-08-19 13:23:48 chinaXiv:202105.00070v2 查看此版本 下载全文
[V1] 2021-05-21 11:51:15 chinaXiv:202105.00070v1 查看此版本 下载全文
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