标题： 从真实数据估计Fisher信息的非参数方法 显示英文标题

标题： Non-parametric estimation of Fisher information from real data

摘要： Fisher信息矩阵是一种广泛应用于统计推断、信息几何、实验设计以及生物系统临界性研究等诸多领域的度量工具。然而，目前尚无一种被普遍接受的非参数算法可以从真实数据中估计它。 在这篇快速通信中，我们展示了如何以非参数的方式准确估计Fisher信息。我们还开发了一种数值方法，通过选择计算Fisher信息定义中导数所需的有限差分方案的区间来最小化误差。 我们的方法使用了最近发布的“利用场论进行密度估计”算法来计算连续密度的概率密度函数。我们用正态分布的Fisher信息来验证我们的方法，并以二维Ising模型为例，计算了Fisher信息矩阵的温度分量，证明其符合与热容的关系，并在正确的临界温度处出现峰值。 显示英文摘要

摘要： The Fisher Information matrix is a widely used measure for applications ranging from statistical inference, information geometry, experiment design, to the study of criticality in biological systems. Yet there is no commonly accepted non-parametric algorithm to estimate it from real data. In this rapid communication we show how to accurately estimate the Fisher information in a nonparametric way. We also develop a numerical procedure to minimize the errors by choosing the interval of the finite difference scheme necessary to compute the derivatives in the definition of the Fisher information. Our method uses the recently published "Density Estimation using Field Theory" algorithm to compute the probability density functions for continuous densities. We use the Fisher information of the normal distribution to validate our method and as an example we compute the temperature component of the Fisher Information Matrix in the two dimensional Ising model and show that it obeys the expected relation to the heat capacity and therefore peaks at the phase transition at the correct critical temperature.