用神经网络+路径采样，从实验数据估算信息传输速率
ML-PWS: Estimating the Mutual Information Between Experimental Time Series Using Neural Networks
- 用生成模型拟合时间序列，再结合路径采样计算下界
- 在非线性模拟数据上与真实值高度一致，误差小于5%
- 适合无先验模型的神经信号等复杂系统分析
量化信息传递能力对自然与工程系统分析和设计至关重要。对于受时变信号驱动的系统，核心度量是信息传输率。然而，由于信号轨迹空间维度高，仅凭时间序列数据无法直接计算该速率，需依赖近似方法。路径加权采样（PWS）是一种计算任意随机模型信息率的精确方法，但如何在缺乏先验模型的情况下从时间序列数据中确定该速率仍是一个问题。本文提出一种结合机器学习（ML）与PWS的方法：从时间序列数据中学习生成模型，并对之应用PWS，从而获得信息率的严格下界。我们在多个非线性模型生成的合成数据上验证了该方法的准确性，结果与直接对模型应用PWS所得真实值高度一致。此外，我们将该方法应用于神经元时间序列数据，展示了其实际效用。
原文摘要 · Abstract (English)
The ability to quantify information transmission is crucial for the analysis and design of both natural and engineered systems. For systems driven by time-varying signals, the fundamental measure is the information transmission rate. However, due to the high dimensionality of signal trajectory space, this rate cannot be obtained directly from time-series data without approximations. Path Weight Sampling (PWS) is a computational technique that enables the exact calculation of the information rate for any stochastic model, raising the question of how this rate can be determined from time-series data in the absence of a prior model. Here, we present a method that combines machine learning (ML) with PWS: a generative model is learned from time-series data, to which PWS is applied to yield a rigorous lower bound on the information rate. We demonstrate the accuracy of this technique, called ML-PWS, by comparing its results on synthetic time-series data generated from several non-linear models against ground-truth results obtained by applying PWS directly to the same models. We illustrate the utility of ML-PWS by applying it to neuronal time-series data.
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