Uncertainty Assessment and False Discovery Rate Control in HighDimensional Granger Causal Inference
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Proceedings of the 34th International Conference on Machine Learning, PMLR 70:684693, 2017.
Abstract
Causal inference among highdimensional time series data proves an important research problem in many fields. While in the classical regime one often establishes causality among time series via a concept known as “Granger causality,” existing approaches for Granger causal inference in highdimensional data lack the means to characterize the uncertainty associated with Granger causality estimates (e.g., pvalues and confidence intervals). We make two contributions in this work. First, we introduce a novel asymptotically unbiased Granger causality estimator with corresponding test statistics and confidence intervals to allow, for the first time, uncertainty characterization in highdimensional Granger causal inference. Second, we introduce a novel method for false discovery rate control that achieves higher power in multiple testing than existing techniques and that can cope with dependent test statistics and dependent observations. We corroborate our theoretical results with experiments on both synthetic data and realworld climatological data.
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