title: Bias reduction in the estimation of mutual information.
abstract: This paper deals with the control of bias estimation when estimating mutual information from a nonparametric approach. We focus on continuously distributed random data and the estimators we developed are based on a nonparametric k-nearest-neighbor approach for arbitrary metrics. Using a multidimensional Taylor series expansion, a general relationship between the estimation error bias and the neighboring size for the plug-in entropy estimator is established without any assumption on the data for two different norms. The theoretical analysis based on the maximum norm developed coincides with the experimental results drawn from numerical tests made by Kraskov et al. [Phys. Rev. E 69, 066138 (2004)PLEEE81539-375510.1103/PhysRevE.69.066138]. To further validate the novel relation, a weighted linear combination of distinct mutual information estimators is proposed and, using simulated signals, the comparison of different strategies allows for corroborating the theoretical analysis.
authors.affiliation: INSERM, U 1099, Rennes, F-35000, France and Université de Rennes 1, LTSI, F-35000, France and Centre de Recherche en Information Biomédicale sino-français (CRIBs), Rennes, France.
authors.forename: Jie
authors.initials: J
authors.lastname: Zhu
authors.affiliation: INSERM, U 1099, Rennes, F-35000, France and Université de Rennes 1, LTSI, F-35000, France.
authors.forename: Jean-Jacques
authors.initials: JJ
authors.lastname: Bellanger
authors.affiliation: Centre de Recherche en Information Biomédicale sino-français (CRIBs), Rennes, France and LIST, School of Computer Science and Engineering, Southeast University, Nanjing, China.
authors.forename: Huazhong
authors.initials: H
authors.lastname: Shu
authors.affiliation: Centre de Recherche en Information Biomédicale sino-français (CRIBs), Rennes, France and LIST, School of Computer Science and Engineering, Southeast University, Nanjing, China.
authors.forename: Chunfeng
authors.initials: C
authors.lastname: Yang
authors.affiliation: INSERM, U 1099, Rennes, F-35000, France and Université de Rennes 1, LTSI, F-35000, France and Centre de Recherche en Information Biomédicale sino-français (CRIBs), Rennes, France.
authors.forename: Régine
authors.initials: R
authors.lastname: Le Bouquin Jeannès