TL;DR
This paper introduces a novel multi-view causal discovery framework that relaxes traditional non-Gaussianity assumptions, enabling causal inference in systems with multiple related data views, validated through simulations and neuroimaging applications.
Contribution
It extends linear SEMs to multi-view data, proves model identifiability under weak assumptions, and develops new algorithms inspired by existing single-view methods.
Findings
Model identifiability for acyclic SEMs with multiple views.
Successful causal graph estimation in neuroimaging data.
Validation through simulations demonstrating effectiveness.
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…
Peer Reviews
Decision·Submitted to ICLR 2026
This article addresses the challenging problem of causal discovery, which traditionally relies on strong assumptions like non-Gaussianity. The authors introduce a novel approach that leverages multi-view data.
I have a concern regarding the step in the identifiability proof where independence is concluded from the vanishing covariances. As is well-known, vanishing covariance does not generally imply independence. Since the proof seems to leverage this implication, its validity depends critically on the underlying distributional assumptions. Please clarify how the non-Gaussianity of the disturbances, potentially via the framework of the Darmois–Skitovich theorem, guarantees that this implication holds
- The paper delivers a significant contribution by establishing the identifiability of linear SEMs using only second-order statistics, eliminating the reliance on non-Gaussianity - The generalization of DirectLiNGAM and PairwiseLiNGAM to the multi-view setting is addressed in a thoughtful manner, yielding novel fast SOS-based algorithms. Additionally, the adaptation of ICA-LiNGAM methodology to accommodate multi-view shared disturbances is conceptually elegant. - The paper is well-organized and
- What is the difference between Ghassami[1] and Perry[2] in this paper? - In Section 3, It would be better that the assumption, "All adjacency matrices ${B}_i$ share the same causal ordering" be explicitly highlighted (or formal definition). - The definitions of some superscripts and subscripts in the text are easily confusing. For example, in Equation (8) of Section 4.5, which represents different views, the superscripts $i$ and $i'$ hinder readability. - In Section C.2，Why is matrix $B$ i
a. The multi-view setting is both common and important. This paper extends two single-view causal-discovery algorithms to the multi-view case and removes the need for non-Gaussian noise assumptions. b. The estimators are fast and straightforward: closed-form likelihood-ratio and cross-covariance tests within a recursive-residual scheme, followed by joint FGLS for edge weights, essentially no tuning required. c. The real-world experiments are good, including MEG/fMRI case studies with cross-sub
a. The contribution is close to existing multi-environment/multi-domain lines. Several works also target identification of linear systems in multi-view or multi-domain settings but are not discussed. For example, [1] addresses causal structure learning for linear relations without relying on non-Gaussian noise or inter-view correlation; [2] studies identification under heterogeneous/noise-variance shifts across domains; and invariance-based approaches such as [3] provide a related lens on levera
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