# GLACIAL: Granger and Learning-based Causality Analysis for Longitudinal Imaging Studies

arXiv: https://arxiv.org/abs/2210.07416 · HTML: https://mlsanity.com/paper/2210.07416/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 79 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [EDDI: Efficient Dynamic Discovery of High-Value Information with Partial VAE](https://mlsanity.com/paper/1809.11142/) (2018)
- [VAEM: a Deep Generative Model for Heterogeneous Mixed Type Data](https://mlsanity.com/paper/2006.11941/) (2020)
- [Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality](https://mlsanity.com/paper/1911.09879/) (2019)
- [Causal Discovery in the Presence of Missing Data](https://mlsanity.com/paper/1807.04010/) (2018)
- [Identifiable Generative Models for Missing Not at Random Data Imputation](https://mlsanity.com/paper/2110.14708/) (2021)
- [Entropic Causal Inference](https://mlsanity.com/paper/1611.04035/) (2016)
- [Fast Causal Inference with Non-Random Missingness by Test-Wise Deletion](https://mlsanity.com/paper/1705.09031/) (2017)
- [Causal structure learning from time series: Large regression coefficients may predict causal links better in practice than small p-values](https://mlsanity.com/paper/2002.09573/) (2020)
- [Simultaneous Missing Value Imputation and Structure Learning with Groups](https://mlsanity.com/paper/2110.08223/) (2021)

## Built on by (most cited first, 1 of 1)

- [Causal Transfer in Medical Image Analysis](https://mlsanity.com/paper/2603.24388/) (2026)

## Abstract (arXiv)

The Granger framework is useful for discovering causal relations in time-varying signals. However, most Granger causality (GC) methods are developed for densely sampled timeseries data. A substantially different setting, particularly common in medical imaging, is the longitudinal study design, where multiple subjects are followed and sparsely observed over time. Longitudinal studies commonly track several biomarkers, which are likely governed by nonlinear dynamics that might have subject-specific idiosyncrasies and exhibit both direct and indirect causes. Furthermore, real-world longitudinal data often suffer from widespread missingness. GC methods are not well-suited to handle these issues. In this paper, we propose an approach named GLACIAL (Granger and LeArning-based CausalIty Analysis for Longitudinal studies) to fill this methodological gap by marrying GC with a multi-task neural forecasting model. GLACIAL treats subjects as independent samples and uses the model's average prediction accuracy on hold-out subjects to probe causal links. Input dropout and model interpolation are used to efficiently learn nonlinear dynamic relationships between a large number of variables and to handle missing values respectively. Extensive simulations and experiments on a real longitudinal medical imaging dataset show GLACIAL beating competitive baselines and confirm its utility. Our code is available at https://github.com/mnhng/GLACIAL.