论文标题
部分可观测时空混沌系统的无模型预测
Minimum-entropy causal inference and its application in brain network analysis
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Identification of the causal relationship between multivariate time series is a ubiquitous problem in data science. Granger causality measure (GCM) and conditional Granger causality measure (cGCM) are widely used statistical methods for causal inference and effective connectivity analysis in neuroimaging research. Both GCM and cGCM have frequency-domain formulations that are developed based on a heuristic algorithm for matrix decompositions. The goal of this work is to generalize GCM and cGCM measures and their frequency-domain formulations by using a theoretic framework for minimum entropy (ME) estimation. The proposed ME-estimation method extends the classical theory of minimum mean squared error (MMSE) estimation for stochastic processes. It provides three formulations of cGCM that include Geweke's original time-domain cGCM as a special case. But all three frequency-domain formulations of cGCM are different from previous methods. Experimental results based on simulations have shown that one of the proposed frequency-domain cGCM has enhanced sensitivity and specificity in detecting network connections compared to other methods. In an example based on in vivo functional magnetic resonance imaging, the proposed frequency-domain measure cGCM can significantly enhance the consistency between the structural and effective connectivity of human brain networks.
