Recovering the directed acyclic graph (DAG) of a structural equation model (SEM) from observational data is a central problem in causal discovery. The iterative gradient descent and per-problem hyperparameter tuning of continuous-optimization methods are poorly suited to two practically important regimes: the sample-limited regime, where the number of samples is comparable to or smaller than the number of nodes in the DAG, and the compute-limited regime. This work proposes SURE-Ridge, a non-iterative, closed-form estimator for equal variance linear Gaussian SEM. The method performs parallel node-wise regressions with regularization parameters chosen adaptively by Stein's unbiased risk estimate (SURE), and applies an adaptive thresholding procedure to extract a DAG from the resulting soft adjacency matrix. Numerical results show that SURE-Ridge achieves the lowest structural Hamming distance in the small-sample regime and the lowest run time across all sample sizes tested, compared with NOTEARS, DAGMA, and GBNSL baselines.
Bayesian causal discovery seeks to determine the posterior distribution of causal theories, which are interpreted as directed acyclic graphs (DAGs) that explain the observed data. The resulting posterior allows systematic reasoning regarding epistemic uncertainty within these theories. Nonetheless, finding such graphs is difficult due to identifiability problems and limited observational data. Furthermore, precisely approximating posterior over graphs is challenging given vast range of potential DAGs. Recent Bayesian approaches have addressed some of these challenges, yet they remain limited as they fail to encode dependencies between edges, and lack principled ways to incorporate domain knowledge as inductive biases during the search process. To overcome these limitations, we propose SVI-DAG, a structured variational inference approach to Bayesian causal discovery using observational data and prior beliefs that uses normalizing flows to model dependencies between edges, supporting expressive and multimodal posterior learning over DAGs. To mitigate mode seeking behaviour in evidence lower bound optimization and promote mode coverage, we use stein variational gradient descent to update the node potentials using a kernel in acyclicity space. We evaluate SVI-DAG against 5 state-of-the-art Bayesian DAG learning methods and demonstrate superior performance in uncertainty quantification while remaining competitive in terms of structural accuracy.
Causal discovery from observational tabular data remains fundamentally challenging, primarily due to the heterogeneity of underlying causal mechanisms and the high-dimensional combinatorial search space of Directed Acyclic Graphs (DAGs). In this paper, we propose \textbf{DAG-FM}, a novel foundation model architecture that amortizes causal discovery. Unlike direct matrix prediction, DAG-FM decomposes the causal discovery process into two auto-regressive stages using two specialized Transformer-based sub-modules: a leaf-node predictor and a parent-node predictor. To effectively model complex row-column interactions, we adopt a robust tabular interaction block to output feature-wise representations. Crucially, to handle diverse and unknown Functional Causal Model (FCM) assumptions in real-world scenarios, we introduce Mixture-of-Leaf-Experts (MoLE), allowing the model to dynamically route and adapt to identifiable mechanism families. Through an iterative inference algorithm, DAG-FM seamlessly extracts causal orderings and constructs valid DAGs. Extensive experiments demonstrate that DAG-FM achieves state-of-the-art performance on both synthetic benchmarks and complex real-world datasets, significantly outperforming traditional classical algorithms and recent foundation models in both accuracy and scalability.
Recovering the exact directed acyclic graph (DAG) in linear non-Gaussian acyclic models with latent confounders (LvLiNGAM) remains a challenging problem. Although LvLiNGAM is identifiable only up to an observational equivalence class, each equivalence class is characterized by a unique sparsest DAG. Recovering the sparsest DAG from finite samples, however, remains difficult. Although existing methods are asymptotically consistent, they do not provide an explicit finite-sample procedure for recovering the unique sparsest DAG, nor do they handle models with an arbitrary number of latent confounders. In this paper, we propose a finite-sample method for recovering the sparsest DAG without imposing any restriction on the number of latent confounders. Simulation studies and real-data analyses demonstrate that the proposed method achieves superior finite-sample performance compared with existing approaches.
We propose \textbf{CaSPECT}, a causal spectral clustering framework for discovering causally homogeneous subgroups from observational data. Rather than clustering in covariate space, CaSPECT defines similarity through the topology of a learned directed acyclic graph (DAG); a bootstrap-stabilised PC algorithm recovers the causal skeleton; a novel \emph{Orientation Validation Score} (OVS) combines PC bootstrap evidence with DirectLiNGAM to orient edges robustly; directed edges are weighted by backdoor-identified average treatment effects estimated via OLS or double machine learning. Chung's directed Laplacian provides a spectral embedding in which individuals close together share the same causal propagation pathways. We establish almost-sure consistency of the full pipeline and validate the method through a controlled simulation study and on LaLonde CPS1, IHDP, and 401(k) datasets, where CaSPECT recovers a positive and statistically significant treatment effect within the causally comparable subpopulation and corrects for severe confounding without requiring a pre-specified propensity score model.