Discovering Instantaneous Granger Causalities in Non-stationary Categorical Time Series Data

Abstract

Instantaneous Granger causality has been used in economy and physiological systems as a measure for quantifying directed effects from prior and contemporary observations to observations in the future. However, standard approaches are mostly unable to capture the instantaneous and the Granger causality together in non-stationary categorical time series where the exact order in which past observations occur has no influence on the causality. In this paper, we propose a novel machine learning-based instantaneous Granger causality (IGC) method that summarizes the past of the cause time series ignoring the temporal order of past observations within a window, and quantifies the dependency between these summaries and the effect time series at each time point independently. Furthermore, our approach allows monitoring the evolution of IGC over time. We apply our method on behavioral data collected from 76 participants in an auditory category learning experiment. The learning process can be seen as an evolution in the ‘decision policies’ across trials, where the current policy is derived from prior stimuli and (accumulated feedback to) prior responses of the participant. The dependency of the current response on the prior exposure to the stimuli and the subsequent responses makes IGC a useful tool in analyzing how the stimulus features contribute to the decision policy: we demonstrate that the instantaneous Granger causalities between stimulus features and responses can distinguish learners from non-learners at early phases of the experiment. Our evaluation shows that our new method outperforms the typically used approach ‘Instantaneous Transfer Entropy’ ($I\mathcal {T}E$).