Multi-View Causal Discovery without Non-Gaussianity: Identifiability and Algorithms

Ambroise Heurtebise, Omar Chehab, Pierre Ablin, Alexandre Gramfort, Aapo Hyvarinen

Abstract: Causal discovery is a difficult problem that typically relies on strong assumptions on the data-generating model, such as non-Gaussianity. In practice, many modern applications provide multiple related views of the same system, which has rarely been considered for causal discovery. Here, we leverage this multi-view structure to achieve causal discovery with weak assumptions. We propose a multi-view linear Structural Equation Model (SEM) that extends the well-known framework of non-Gaussian disturbances by alternatively leveraging correlation over views. We prove the identifiability of the model for acyclic SEMs. Subsequently, we propose several multi-view causal discovery algorithms, inspired by single-view algorithms (DirectLiNGAM, PairwiseLiNGAM, and ICA-LiNGAM). The new methods are validated through simulations and applications on neuroimaging data, where they enable the estimation of causal graphs between brain regions.

Lay Summary: Understanding which data variables cause which, based solely on analysis of the data without any further information, is a hard problem. To accomplish such causal discovery, we leverage a particular structure: in many modern applications, the same system is measured simultaneously from multiple views or using different devices, creating correlated datasets. This allows causal discovery under weak assumptions, enabling for example the discovery of causal relationships between brain regions from neuroimaging data.

Link To Code: https://github.com/AmbroiseHeurtebise/LiMVAM

Primary Area: General Machine Learning->Causality

Keywords: Causal discovery, Independent component analysis, Non-Gaussianity, Multiview data, Second-order statistics

Submission Number: 19222