CoLiDE: Concomitant Linear DAG Estimation

• URL: http://arxiv.org/abs/2310.02895v2
• Date: Wed, 13 Mar 2024 14:56:11 GMT
• Title: CoLiDE: Concomitant Linear DAG Estimation
• Authors: Seyed Saman Saboksayr, Gonzalo Mateos, Mariano Tepper
• Abstract summary: We deal with the problem of learning acyclic graph structure from observational data to a linear equation. We propose a new convex score function for sparsity-aware learning DAGs.
• Score: 12.415463205960156
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We deal with the combinatorial problem of learning directed acyclic graph (DAG) structure from observational data adhering to a linear structural equation model (SEM). Leveraging advances in differentiable, nonconvex characterizations of acyclicity, recent efforts have advocated a continuous constrained optimization paradigm to efficiently explore the space of DAGs. Most existing methods employ lasso-type score functions to guide this search, which (i) require expensive penalty parameter retuning when the $\textit{unknown}$ SEM noise variances change across problem instances; and (ii) implicitly rely on limiting homoscedasticity assumptions. In this work, we propose a new convex score function for sparsity-aware learning of linear DAGs, which incorporates concomitant estimation of scale and thus effectively decouples the sparsity parameter from the exogenous noise levels. Regularization via a smooth, nonconvex acyclicity penalty term yields CoLiDE ($\textbf{Co}$ncomitant $\textbf{Li}$near $\textbf{D}$AG $\textbf{E}$stimation), a regression-based criterion amenable to efficient gradient computation and closed-form estimation of noise variances in heteroscedastic scenarios. Our algorithm outperforms state-of-the-art methods without incurring added complexity, especially when the DAGs are larger and the noise level profile is heterogeneous. We also find CoLiDE exhibits enhanced stability manifested via reduced standard deviations in several domain-specific metrics, underscoring the robustness of our novel linear DAG estimator.

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