REGO: Rank-based Estimation of Renyi Information using Euclidean Graph Optimization

We propose a new method for a non- parametric estimation of Renyi and Shan- non information for a multivariate distribu- tion using a corresponding copula, a multi- variate distribution over normalized ranks of the data. As the information of the distri- bution is the same as the negative entropy of its copula, our method estimates this in- formation by solving a Euclidean graph opti- mization problem on the empirical estimate of the distribution's copula. Owing to the properties of the copula, we show that the resulting estimator of Renyi information is strongly consistent and robust. Further, we demonstrate its applicability in image regis- tration in addition to simulated experiments.

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