Deep recurrent modelling of Granger causality with latent confounding

Inferring causal relationships in observational time series data is an important task when interventions cannot be performed. Granger causality is a popular framework to infer potential causal mechanisms between different time series. The original definition of Granger causality is restricted to linear processes and leads to spurious conclusions in the presence of a latent confounder. To this end, we propose a deep learning model to detect non-linear Granger causality and directly account for latent confounders. Our approach consists of two components: 1. feed-forward neural networks to infer representations of the confounder from available proxy variables; 2. recurrent neural networks to construct forecasting models for the target time series with and without additional information. Conditioned on the proxy, if the target time series can be better predicted without extra information, our model concludes that the confounder alone Granger causes the target, and vice versa. To assess the proposed approach, we tested the model on both synthetic and real world time series with known causal relationships; results showed the superiority of our model relative to existing benchmarks.