opula熵：理论和应用

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.