Induced Covariance for Causal Discovery in Linear Sparse Structures
Saeed Mohseni-Sehdeh, Walid Saad
TL;DR
This paper presents a new causal discovery algorithm for linear sparse structures that leverages structural matrices and their statistical properties, outperforming existing methods without relying on independence tests.
Contribution
The novel algorithm identifies causal structures in linear sparse settings using structural matrices, avoiding independence tests and graph fitting, suitable for limited data scenarios.
Findings
Outperforms PC, GES, BIC, and LINGAM in recovering sparse causal structures
Does not rely on independence tests or graph fitting procedures
Effective with limited training data
Abstract
Causal models seek to unravel the cause-effect relationships among variables from observed data, as opposed to mere mappings among them, as traditional regression models do. This paper introduces a novel causal discovery algorithm designed for settings in which variables exhibit linearly sparse relationships. In such scenarios, the causal links represented by directed acyclic graphs (DAGs) can be encapsulated in a structural matrix. The proposed approach leverages the structural matrix's ability to reconstruct data and the statistical properties it imposes on the data to identify the correct structural matrix. This method does not rely on independence tests or graph fitting procedures, making it suitable for scenarios with limited training data. Simulation results demonstrate that the proposed method outperforms the well-known PC, GES, BIC exact search, and LINGAM-based methods in…
Peer Reviews
Decision·Submitted to ICLR 2026
The paper introduces a novel approach to causal structure estimation based on the concept of induced covariance, offering a fresh perspective distinct from traditional statistical causal discovery methods. It demonstrates that, under the assumption of sparsity in the causal structure, the proposed method can accurately recover causal graphs even with a limited number of samples. This contributes to expanding the applicability of causal discovery to real-world scenarios where sample sizes are oft
The paper lacks sufficient explanation of several critical assumptions, which raises major concerns about the soundness of its theoretical development. In particular, the derivation from Equation (7) to Equation (10) assumes that the variables $x_i$ are largely uncorrelated implicitly; without this assumption, the equations do not hold as presented. While such an assumption would make the derivation understandable, the paper provides almost no discussion of it. As a result, readers may struggle
Unfortunately, I find no obvious strength of this paper.
1. The theoretical results in this paper cannot demonstrate the superiority of their proposed SLCD. - Both Theorem 3 and Theorem 4 assume there is a solution $D$ s.t. $F(D) = 0$ and $DX = X$. However, such a $D$ does not exists if there are noise terms, which is a standard setting in the previous literature on causality. - Even there exists such a $D$, Theorem 3 and Theorem 4 only demonstrate that two solutions $D, D'$ s.t. $F(D) = F(D') = 0$ and $D X = D' X = X$ are close to each other, whic
a. Introduces a new formulation for structure learning that leverages second-order constraints, avoiding conditional independence tests. b. The proposed optimization objective is intuitive, combining covariance factorization and data reconstruction with sparsity-promoting penalties. c. Theoretical results show local uniqueness of the true structural matrix under certain conditions. d. Experiments on simulated data suggest improved recovery of sparse DAGs in low-sample regimes.
a. Theorem 1, which establishes the covariance factorization $\Sigma = D \sigma D^T$, is not new and was previously formalized in, e.g., Sullivant et al. (2010) through trek separation theory. The paper should clearly cite this foundational work. b. The main theoretical guarantee shows only local uniqueness, not global identifiability. This means alternative structures could still satisfy the constraints elsewhere in the parameter space, so identifiability is not ensured in the full sense. c.
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Taxonomy
TopicsGeochemistry and Geologic Mapping · Data Quality and Management · Rough Sets and Fuzzy Logic