Inferring Causality from Time Series data based on Structural Causal Model and its application to Neural Connectomics

Abstract: Inferring causation from time series data is of scientific interest in different disciplines, particularly in neural connectomics. While different approaches exist in the literature with parametric modeling assumptions, we focus on a non-parametric model for time series satisfying a Markovian structural causal model with stationary distribution and without concurrent effects. We show that the model structure can be used to its advantage to obtain an elegant algorithm for causal inference from time series based on conditional dependence tests, coined Causal Inference in Time Series (CITS) algorithm. We describe Pearson's partial correlation and Hilbert-Schmidt criterion as candidates for such conditional dependence tests that can be used in CITS for the Gaussian and non-Gaussian settings, respectively. We prove the mathematical guarantee of the CITS algorithm in recovering the true causal graph, under standard mixing conditions on the underlying time series. We also conduct a comparative evaluation of performance of CITS with other existing methodologies in simulated datasets. We then describe the utlity of the methodology in neural connectomics -- in inferring causal functional connectivity from time series of neural activity, and demonstrate its application to a real neurobiological dataset of electro-physiological recordings from the mouse visual cortex recorded by Neuropixel probes.