Uncertainty-Aware Granger Causality from Irregular Time Series

Granger causality (GC) is a fundamental tool for identifying directional dependencies in time series, yet most existing methods assume regularly sampled observations. This assumption limits their applicability to real-world data, which are often irregularly sampled and contain unknown missing values. We address GC detection under these conditions by combining a Gaussian process (GP)--based representation with a nonlinear GC inference framework. Specifically, we adopt an uncertainty-aware representation based on GP posteriors and Expected Gaussian Kernel (EGK) features, originally proposed for irregular time-series modeling, and integrate it into a causality detection pipeline. Using random Fourier and Fastfood approximations, we transform irregular time series into regular feature sequences suitable for nonlinear GC testing. Experiments on simulated data show that explicitly propagating posterior uncertainty improves causal detection under moderate to severe missingness. On real-world datasets, the proposed approach produces stable and interpretable causality estimates with performance comparable to established baselines, while avoiding overconfident inference under irregular sampling. These results highlight the importance of uncertainty-aware representations for reliable Granger causality analysis in irregularly sampled time series.