Evaluation of Mutual Information Estimators for Time Series - Physics > Data Analysis, Statistics and ProbabilityReport as inadecuate




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Abstract: We study some of the most commonly used mutual information estimators, basedon histograms of fixed or adaptive bin size, $k$-nearest neighbors and kernels,and focus on optimal selection of their free parameters. We examine theconsistency of the estimators convergence to a stable value with the increaseof time series length and the degree of deviation among the estimators. Theoptimization of parameters is assessed by quantifying the deviation of theestimated mutual information from its true or asymptotic value as a function ofthe free parameter. Moreover, some common-used criteria for parameter selectionare evaluated for each estimator. The comparative study is based on Monte Carlosimulations on time series from several linear and nonlinear systems ofdifferent lengths and noise levels. The results show that the $k$-nearestneighbor is the most stable and less affected by the method-specific parameter.A data adaptive criterion for optimal binning is suggested for linear systemsbut it is found to be rather conservative for nonlinear systems. It turns outthat the binning and kernel estimators give the least deviation in identifyingthe lag of the first minimum of mutual information from nonlinear systems, andare stable in the presence of noise.



Author: Angeliki Papana, Dimitris Kugiumtzis

Source: https://arxiv.org/







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