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An Approximation Scheme for Multivariate Information based on Partial Information Decomposition

We consider an approximation scheme for multivariate information assuming that synergistic information only appearing in higher order joint distributions is suppressed, which may hold in large classes of systems. Our approximation scheme gives a practical way to evaluate information among random variables and is expected to be applied to feature selection in machine learning. The truncation order of our approximation scheme is given by the order of synergy. In the classification of information, we use the partial information decomposition of the original one. The resulting multivariate information is expected to be reasonable if higher order synergy is suppressed in the system. In addition, it is calculable in relatively easy way if the truncation order is not so large. We also perform numerical experiments to check the validity of our approximation scheme.