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“…To the best of our knowledge, there is a blank in the field of optimal bandwidth selection in kernel-based TE estimator. As He et al [37] show, when estimating the entropy estimator, two types of errors would be generated, one is from entropy estimation and the other from density estimation, and the optimal bandwidth for density estimation may not coincide with the optimal one for entropy estimation. Thus, rather than the rule-of-thumb bandwidth in [33], which aims at optimal density estimation, the bandwidth in our study should provide an accurate estimator for I(Z, X|Y) in the minimal mean squared error (MSE) sense, say.…”
Section: Theoremmentioning
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“…To the best of our knowledge, there is a blank in the field of optimal bandwidth selection in kernel-based TE estimator. As He et al [37] show, when estimating the entropy estimator, two types of errors would be generated, one is from entropy estimation and the other from density estimation, and the optimal bandwidth for density estimation may not coincide with the optimal one for entropy estimation. Thus, rather than the rule-of-thumb bandwidth in [33], which aims at optimal density estimation, the bandwidth in our study should provide an accurate estimator for I(Z, X|Y) in the minimal mean squared error (MSE) sense, say.…”
Section: Theoremmentioning
“…Estimation of parameters and testing of hypothesis are the two cornerstones of modern statistics [9]. From statisticians their point of view, all data are classified into different types of distribution using statistical analysis.…”
Section: Introductionmentioning
“…Specifically, we want to clarify the influence of variances of random weights and biases on the training and testing accuracies of ELM. Three mostly-used continuous probability distributions [16], i.e., Uniform, Gamma and Normal, are employed in our study to initialize the input-layer weights and hidden-layer biases for ELMs. For each distribution, 6 different parameter pairs are initialized as shown in Fig.…”
Section: Introductionmentioning