# Large-scale kernelized GRANGER causality to infer topology of directed graphs with applications to brain networks

arXiv: https://arxiv.org/abs/2011.08261 · HTML: https://mlsanity.com/paper/2011.08261/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2020.

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

- [Large-Scale Extended Granger Causality for Classification of Marijuana Users From Functional MRI](https://mlsanity.com/paper/2101.01832/) (2021)
- [Large-scale Augmented Granger Causality (lsAGC) for Connectivity Analysis in Complex Systems: From Computer Simulations to Functional MRI (fMRI)](https://mlsanity.com/paper/2101.09354/) (2021)
- [Classification of Schizophrenia from Functional MRI Using Large-scale Extended Granger Causality](https://mlsanity.com/paper/2101.10471/) (2021)
- [An Unbiased Symmetric Matrix Estimator for Topology Inference under Partial Observability](https://mlsanity.com/paper/2203.15500/) (2022)
- [Re-defining Radiology Quality Assurance (QA) -- Artificial Intelligence (AI)-Based QA by Restricted Investigation of Unequal Scores (AQUARIUS)](https://mlsanity.com/paper/2205.00629/) (2022)
- [Cross Modal Global Local Representation Learning from Radiology Reports and X-Ray Chest Images](https://mlsanity.com/paper/2301.10951/) (2023)
- [Enhancing Graph Attention Neural Network Performance for Marijuana Consumption Classification through Large-scale Augmented Granger Causality (lsAGC) Analysis of Functional MR Images](https://mlsanity.com/paper/2410.18506/) (2024)
- [CAARL: In-Context Learning for Interpretable Co-Evolving Time Series Forecasting](https://mlsanity.com/paper/2604.18305/) (2026)

## Abstract (arXiv)

Graph topology inference of network processes with co-evolving and interacting time-series is crucial for network studies. Vector autoregressive models (VAR) are popular approaches for topology inference of directed graphs; however, in large networks with short time-series, topology estimation becomes ill-posed. The present paper proposes a novel nonlinearity-preserving topology inference method for directed networks with co-evolving nodal processes that solves the ill-posedness problem. The proposed method, large-scale kernelized Granger causality (lsKGC), uses kernel functions to transform data into a low-dimensional feature space and solves the autoregressive problem in the feature space, then finds the pre-images in the input space to infer the topology. Extensive simulations on synthetic datasets with nonlinear and linear dependencies and known ground-truth demonstrate significant improvement in the Area Under the receiver operating characteristic Curve ( AUC ) of the receiver operating characteristic for network recovery compared to existing methods. Furthermore, tests on real datasets from a functional magnetic resonance imaging (fMRI) study demonstrate 96.3 percent accuracy in diagnosis tasks of schizophrenia patients, which is the highest in the literature with only brain time-series information.