时间序列互信息估计量的评价
Evaluation of Mutual Information Estimators for Time Series
摘要：
我们研究了一些最常用的互信息估计，基于直方图的固定或自适应箱大小，$k$ -最近邻和内核，并专注于其自由参数的最佳选择。我们检查了估计量的一致性（随着时间序列长度的增加收敛到稳定值）和估计量之间的偏差程度。参数的优化是通过量化估计的互信息与其真实值或渐近值的偏差作为自由参数的函数来评估的。此外，一些常用的参数选择标准进行评估，为每个估计。比较研究是基于蒙特卡罗模拟的时间序列从几个线性和非线性系统的不同长度和噪声水平。结果表明，$k$ -最近邻是最稳定的，受方法特定参数的影响较小。对于线性系统，提出了一种数据自适应的最优分级准则，但对于非线性系统，该准则是相当保守的。结果表明，在识别非线性系统互信息第一最小值的滞后时，分箱估计和核估计给出了最小偏差，并且在存在噪声的情况下是稳定的。
英文摘要：
We study some of the most commonly used mutual information estimators, based on histograms of fixed or adaptive bin size, $k$-nearest neighbors and kernels, and focus on optimal selection of their free parameters. We examine the consistency of the estimators (convergence to a stable value with the increase of time series length) and the degree of deviation among the estimators. The optimization of parameters is assessed by quantifying the deviation of the estimated mutual information from its true or asymptotic value as a function of the free parameter. Moreover, some common-used criteria for parameter selection are evaluated for each estimator. The comparative study is based on Monte Carlo simulations on time series from several linear and nonlinear systems of different lengths and noise levels. The results show that the $k$-nearest neighbor is the most stable and less affected by the method-specific parameter. A data adaptive criterion for optimal binning is suggested for linear systems but it is found to be rather conservative for nonlinear systems. It turns out that the binning and kernel estimators give the least deviation in identifying the lag of the first minimum of mutual information from nonlinear systems, and are stable in the presence of noise.
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