Model selection method based on maximal information coefficient of residuals |
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Authors: | Qiuheng TAN Hangjin JIANG Yiming DING |
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Affiliation: | 1. Wuhan Institute of Physics and Mathematics, CAS, Wuhan 430071, China;2. University of CAS, Beijing 100049, China;3. Key Laboratory of Magnetic Resonance in Biological Systems, Wuhan Institute of Physics and Mathematics, CAS, Wuhan 430071, China;4. National Center for Mathematics and Interdisciplinary Sciences, CAS, Beijing 100049, China |
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Abstract: | The traditional model selection criterions try to make a balance between fitted error and model complexity. Assumptions on the distribution of the response or the noise, which may be misspecified, should be made before using the traditional ones. In this article, we give a new model selection criterion, based on the assumption that noise term in the model is independent with explanatory variables, of minimizing the association strength between regression residuals and the response, with fewer assumptions. Maximal Information Coefficient (MIC), a recently proposed dependence measure, captures a wide range of associations, and gives almost the same score to different type of relationships with equal noise, so MIC is used to measure the association strength. Furthermore, partial maximal information coefficient (PMIC) is introduced to capture the association between two variables removing a third controlling random variable. In addition, the definition of general partial relationship is given. |
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Keywords: | Model Selection residual maximal information coefficient partial maximal information coefficient |
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