On the influence of the kernel on the consistency of support vector machines
The Journal of Machine Learning Research
Efficient svm training using low-rank kernel representations
The Journal of Machine Learning Research
An Invariance Property of Predictors in Kernel-Induced Hypothesis Spaces
Neural Computation
Effective detection of coupling in short and noisy bivariate data
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Neural Computation
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A straightforward nonlinear extension of Granger's concept of causality in the kernel framework is suggested. The kernel-based approach to assessing nonlinear Granger causality in multivariate time series enables us to determine, in a model-free way, whether the causal relation between two time series is present or not and whether it is direct or mediated by other processes. The trace norm of the so-called covariance operator in feature space is used to measure the prediction error. Relying on this measure, we test the improvement of predictability between time series by subsampling-based multiple testing. The distributional properties of the resulting p-values reveal the direction of Granger causality. Experiments with simulated and real-world data show that our method provides encouraging results.