标题： 互信息率 -- 线性噪声近似与精确计算 显示英文标题

标题： Mutual Information Rate -- Linear Noise Approximation and Exact Computation

摘要： 高效的信息处理对于生物有机体和工程系统都是至关重要的。互信息率是信息论中的一个核心概念，它量化了输入和输出信号轨迹之间共享的信息量，并能够对动态系统中的信息流进行量化。估计互信息率的一种常见方法是高斯近似，该方法假设输入和输出轨迹遵循高斯统计特性。然而，这种方法仅适用于线性系统，其在非线性或离散系统中的准确性仍不清楚。在本工作中，我们通过利用路径权重采样（PWS），一种最近用于精确计算互信息率的技术，评估了高斯近似在非高斯系统中的准确性。在两个案例研究中，我们检验了高斯近似的局限性。首先，我们关注离散线性系统，并证明即使系统的统计特性接近高斯分布，高斯近似也无法准确估计互信息率。其次，我们探讨了一个具有非线性传递函数的连续扩散系统，随着非线性的增加，高斯近似与精确的互信息率之间出现了显著偏差。我们的结果对高斯近似在不同随机模型中的性能进行了定量评估，并指出了何时需要使用计算更密集的方法，如PWS。 显示英文摘要

摘要： Efficient information processing is crucial for both living organisms and engineered systems. The mutual information rate, a core concept of information theory, quantifies the amount of information shared between the trajectories of input and output signals, and enables the quantification of information flow in dynamic systems. A common approach for estimating the mutual information rate is the Gaussian approximation which assumes that the input and output trajectories follow Gaussian statistics. However, this method is limited to linear systems, and its accuracy in nonlinear or discrete systems remains unclear. In this work, we assess the accuracy of the Gaussian approximation for non-Gaussian systems by leveraging Path Weight Sampling (PWS), a recent technique for exactly computing the mutual information rate. In two case studies, we examine the limitations of the Gaussian approximation. First, we focus on discrete linear systems and demonstrate that, even when the system's statistics are nearly Gaussian, the Gaussian approximation fails to accurately estimate the mutual information rate. Second, we explore a continuous diffusive system with a nonlinear transfer function, revealing significant deviations between the Gaussian approximation and the exact mutual information rate as nonlinearity increases. Our results provide a quantitative evaluation of the Gaussian approximation's performance across different stochastic models and highlight when more computationally intensive methods, such as PWS, are necessary.