# Deep Recurrent Modelling of Granger Causality with Latent Confounding

arXiv: https://arxiv.org/abs/2202.11286 · HTML: https://mlsanity.com/paper/2202.11286/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 33 references that are in the map.
- First posted on arXiv 23 Feb 2022.

## Builds on (most cited first, 9 of 9)

- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [High-recall causal discovery for autocorrelated time series with latent confounders](https://mlsanity.com/paper/2007.01884/) (2020)
- [Time Series Deconfounder: Estimating Treatment Effects over Time in the Presence of Hidden Confounders](https://mlsanity.com/paper/1902.00450/) (2019)
- [Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality](https://mlsanity.com/paper/1911.09879/) (2019)
- [Interpretable Models for Granger Causality Using Self-explaining Neural Networks](https://mlsanity.com/paper/2101.07600/) (2021)
- [Causal Inference for Time series Analysis: Problems, Methods and Evaluation](https://mlsanity.com/paper/2102.05829/) (2021)
- [Neural Additive Vector Autoregression Models for Causal Discovery in Time Series](https://mlsanity.com/paper/2010.09429/) (2020)
- [The Statistical Recurrent Unit](https://mlsanity.com/paper/1703.00381/) (2017)

## Built on by (most cited first, 8 of 8)

- [Time Series Causal Link Estimation under Hidden Confounding using Knockoff Interventions](https://mlsanity.com/paper/2209.11497/) (2022)
- [DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Series](https://mlsanity.com/paper/2511.02137/) (2025)
- [Semiparametric inference for impulse response functions using double/debiased machine learning](https://mlsanity.com/paper/2411.10009/) (2024)
- [CausalMamba: Scalable Conditional State Space Models for Neural Causal Inference](https://mlsanity.com/paper/2510.17318/) (2025)
- [Causally Linking Health Application Data and Personal Information Management Tools](https://mlsanity.com/paper/2308.08556/) (2023)
- [Emergent Granger Causality in Neural Networks: Can Prediction Alone Reveal Structure?](https://mlsanity.com/paper/2506.20347/) (2025)
- [Temporal Latent Variable Structural Causal Model for Causal Discovery under External Interferences](https://mlsanity.com/paper/2511.10031/) (2025)
- [Latent-Space Causal Discovery from Indirect Neuroimaging Observations](https://mlsanity.com/paper/2602.09034/) (2026)

## Abstract (arXiv)

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. In this work, we harness the expressive power of recurrent neural networks and propose a deep learning-based approach to model non-linear Granger causality by directly accounting for latent confounders. Our approach leverages multiple recurrent neural networks to parameterise predictive distributions and we propose the novel use of a dual-decoder setup to conduct the Granger tests. We demonstrate the model performance on non-linear stochastic time series for which the latent confounder influences the cause and effect with different time lags; results show the effectiveness of our model compared to existing benchmarks.