AI 中文总结
针对脑信号有效连接性估计中高斯残差假设的局限，提出基于一般残差分布信道容量的分布感知度量，并开发双流极小极大估计器，在模拟和真实脑信号中优于现有方法。
AI 中文摘要
从脑信号中估计有效连接性通常依赖于高斯残差建模，这种方法虽然便于估计，但当经验残差非高斯时，可能会丢弃有信息量的分布结构并扭曲推断出的有向交互。我们在多种模态、物种和实验条件下表明，脑信号和拟合的信道残差都经常偏离高斯性。因此，我们引入了一种基于一般残差分布下信道容量的、分布感知的、信息论的有效连接性度量。为了从经验性的、可能非高斯的残差中估计由此产生的容量，我们开发了一种基于归一化流的双流极小极大估计器，其中生成器在功率约束下搜索可容许的输入分布，而观测器则估计输出熵。我们提供了该估计器的理论表征，表明观测器目标可以恢复微分熵，直至一个KL近似项；该公式在特殊情况下可简化为经典高斯容量；残差熵可以改变超出方差的可实现信息速率；博弈差距和误差分析进一步刻画了优化和近似的来源。在具有已知有向连接的脑样模拟中，与高斯容量、格兰杰因果、VAR-LiNGAM和GIMME相比，双流方法在涵盖多样网络拓扑、隐藏驱动、反馈和异质血流动力学的十种条件下取得了最高的AUROC和AUPRC。应用于多模态脑信号时，该方法揭示了与已知神经生物学回路一致的时间和条件分辨的有向交互。总之，这些结果建立了一个原则性的、分布感知的有效连接性估计框架，超越了高斯残差建模。
英文摘要
Effective-connectivity estimation from brain signals often relies on Gaussian residual modeling, which enables tractable estimation but can discard informative distributional structure and distort inferred directed interactions when empirical residuals are non-Gaussian. We show across multiple modalities, species, and experimental conditions that both brain signals and fitted channel residuals frequently deviate from Gaussianity. We therefore introduce a distribution-aware, information-theoretic measure of effective connectivity based on channel capacity under general residual distributions. To estimate the resulting capacity from empirical, potentially non-Gaussian residuals, we develop a dual-flow min-max estimator based on normalizing flows, in which a generator searches over admissible input distributions under a power constraint while an observer estimates output entropy. We provide a theoretical characterization of the estimator, showing that the observer objective recovers differential entropy up to a KL approximation term, that the formulation reduces to classical Gaussian capacity as a special case, and that residual entropy can alter achievable information rates beyond variance; game-gap and error analyses further characterize optimization and approximation sources. In brain-like simulations with known directed connectivity, Dual-flow achieves the highest AUROC and AUPRC across ten conditions spanning diverse network topologies, hidden drivers, feedback, and heterogeneous hemodynamics, compared with Gaussian capacity, Granger causality, VAR-LiNGAM, and GIMME. Applied to multimodal brain signals, the method reveals time- and condition-resolved directed interactions consistent with known neurobiological circuitry. Together, these results establish a principled distribution-aware framework for effective-connectivity estimation beyond Gaussian residual modeling.
Comments31 pages, 9 figures, 5 tables
