Cross-cumulants measure for independence |
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Authors: | Pando Georgiev Anca Ralescu Dan Ralescu |
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Institution: | 1. ECECS Department, University of Cincinnati, ML 0030, Cincinnati, OH 45221-0030, USA;2. Department of Mathematical Sciences, University of Cincinnati, ML 0030, Cincinnati, OH 45221-0030, USA |
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Abstract: | We propose a measure for independence of group of random variables, given by a sum of cross-cumulants of a given order n . A similar measure was known for the case of fourth-order cross-cumulants from the JADE algorithm for ICA (independent component analysis). We derive a formula for its calculation using cumulant tensors. In the case n=4 our formula allows efficient calculation of this measure, using cumulant matrices. Much attention is devoted to the case of six-order cross-cumulants, aiming to show that this measure can be calculated using again cumulant matrices. |
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Keywords: | Primary 62H20 secondary 62H12 |
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