非线性Granger因果关系的核方法
Kernel method for nonlinear Granger causality
摘要：
关于由一个以上组成部分组成的复杂系统的结构的重要信息，可以通过测量各个组成部分相互交换信息的程度来获得。需要这些知识来更深入地理解从湍流流体到神经网络以及复杂的生理信号等现象。线性格兰杰方法，检测时间序列之间的因果关系，近年来已成为一个领先的统计技术来完成这一任务。在这里，我们推广格兰杰因果关系的非线性情况下，使用再生核希尔伯特空间的理论。我们的方法进行线性格兰杰因果关系的特征空间中的合适的核函数，假设任意程度的非线性。我们开发了一种新的策略，以应付过拟合的问题，再生核希尔伯特空间的几何基础上。耦合混沌映射和生理数据集的应用。
英文摘要：
Important information on the structure of complex systems, consisting of more than one component, can be obtained by measuring to which extent the individual components exchange information among each other. Such knowledge is needed to reach a deeper comprehension of phenomena ranging from turbulent fluids to neural networks, as well as complex physiological signals. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and physiological data sets are presented.
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