利用路径权重采样精确计算传递熵
Exact computation of Transfer Entropy with Path Weight Sampling
AI总结：
本文提出TE-PWS算法，首次实现任意随机模型传递熵的精确蒙特卡洛计算，并证明常用近似方法误差大，且揭示反馈下传递熵可超越数据处理不等式。
摘要：
量化信息的定向流动能力对于理解自然系统和设计工程化信息处理系统至关重要。传递熵是一种被广泛用于量化这种信息流动的度量。然而，迄今为止，这一量在动力学模型中只能通过通常不可控的近似方法获得。本文提出了一种名为传递熵-路径权重采样（TE-PWS）的计算算法，该算法首次使得对任意随机模型（包括具有多个隐变量、非线性、瞬态条件和反馈的模型）精确量化传递熵及其变体成为可能。通过利用聚合物和路径采样技术，TE-PWS将传递熵作为信号轨迹空间上的蒙特卡洛平均值高效计算。我们使用这一精确技术证明，常用的近似计算传递熵的方法会产生较大的系统误差和高计算成本。作为应用，我们在线性和非线性系统中使用TE-PWS，揭示了在存在反馈时传递熵如何克服数据处理不等式的朴素应用。
英文摘要：
The ability to quantify the directional flow of information is vital to understanding natural systems and designing engineered information-processing systems. A widely used measure to quantify this information flow is the transfer entropy. However, until now, this quantity could only be obtained in dynamical models using approximations that are typically uncontrolled. Here we introduce a computational algorithm called Transfer Entropy-Path Weight Sampling (TE-PWS), which makes it possible, for the first time, to quantify the transfer entropy and its variants exactly for any stochastic model, including those with multiple hidden variables, nonlinearity, transient conditions, and feedback. By leveraging techniques from polymer and path sampling, TE-PWS efficiently computes the transfer entropy as a Monte-Carlo average over signal trajectory space. We use our exact technique to demonstrate that commonly used approximate methods to compute transfer entropies incur large systematic errors and high computational costs. As an application, we use TE-PWS in linear and nonlinear systems to reveal how transfer entropy can overcome naive applications of the data processing inequality in the presence of feedback.
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