This repository implements the algorithms introduced in this paper.

It provides three main methods: DirectLiMVAM, PairwiseLiMVAM, and ICA-LiMVAM (with its two variants ICA-LiMVAM-J and ICA-LiMVAM-ML).

Given multi-view data (multiple datasets describing the same variables across different views), these algorithms aim to:

• Recover a shared causal ordering of variables across views
• Estimate the strength of causal relationships

All implementations are written in Python and are available in limvam.

From within your local repository, run

pip install -e .

from limvam import direct_limvam
import numpy as np

X = np.random.randn(n_views, n_variables, n_samples)
B, T, P = direct_limvam(X)

In the outputs:

• B are square matrices that contain the strength of causal relationships
• T are strictly lower triangular matrices
• P is a permutation matrix that contains the causal ordering

Three example notebooks are provided in the examples folder. They demonstrate how to use each algorithm in practice on simple synthetic data.

This experiment uses data from a preprocessed dataset.

The dataset contains fMRI recordings from 9 participants who performed a rhyming judgment task. Each participant's recordings contain 9 variables: one task regressor and 8 brain regions. We apply one of our methods to recover a causal graph between brain regions.

The experiment runs quickly and is available in the experiments_fmri folder.

The code to reproduce the MEG experiments is located in the experiments_meg folder. However, running these experiments requires downloading the Cam-CAN dataset and adapting some paths.

The experiments_synthetic folder contains several simulation studies evaluating the methods under different scenarios, including: varying the numbers of views, variables, samples, or the noise level.

If you use this code in your project, please cite this paper:

Ambroise Heurtebise, Omar Chehab, Pierre Ablin, Alexandre Gramfort, Aapo Hyvärinen
Multi-View Causal Discovery without Non-Gaussianity: Identifiability and Algorithms
arXiv preprint, 2025