structural causal modeling

Conventional acyclic acyclic directed mixed graphs (ADMGs) fail to model cyclic causal structures prevalent in high-dimensional dynamical systems—e.g., economics, neuroscience, and control theory—where feedback loops are intrinsic. Method: This paper investigates macro-causal effect identification on clustered directed mixed graphs (C-DMGs) built over input-output structural causal models (ioSCMs) and general directed mixed graphs (DMGs), which explicitly accommodate cycles. Contribution/Results: We establish, for the first time, the soundness and completeness of the do-calculus within this cyclic abstract graphical framework. We generalize non-identifiability criteria from acyclic to a broad subclass of cyclic DMGs. Furthermore, we develop a complete theoretical characterization of macro-causal effect identifiability in C-DMGs over DMGs. By lifting the acyclicity assumption, our work substantially extends the applicability of structural causal inference to realistic, feedback-rich, dynamic systems.

This work addresses the challenge posed by latent variables, which can induce non-directed acyclic and non-unique causal graphs among observed variables, thereby undermining conventional causal invariance methods. The paper characterizes the structure of such latent-induced observational graphs and, for the first time, establishes rigorous necessary and sufficient conditions for causal invariance in settings involving latent confounders, explicitly delineating its applicability even when the observed graph is not a DAG. Under a multivariate Gaussian assumption, the authors develop a verifiable theoretical framework that integrates causal graphical models with hypothesis testing. When the derived conditions hold, this framework accurately identifies observable causal parents, substantially enhancing the reliability of causal discovery in the presence of latent interference.

Direct effect estimation on a selected causal graph induces selection bias due to data reuse, invalidating confidence intervals. Method: We propose the first post-selection inference framework for fixed-population causal effect parameters, integrating resampling with graph-structure screening to depart from the conventional “select-then-infer” paradigm. Built upon the PC algorithm, our approach unifies conditional independence testing, Gaussian modeling, and joint estimation over multiple candidate graphs, and is modularly extensible to other causal discovery algorithms and distribution families. Contribution/Results: We establish asymptotic validity—specifically, asymptotically exact coverage—for confidence sets targeting the true causal effect. Empirical evaluations demonstrate that our method substantially improves reliability and robustness of causal inference under uncertainty, yielding well-calibrated confidence sets even after graph selection.

This paper addresses the problem of identifying the set of direct causes (i.e., local causal structure) of a target variable from purely observational data in a single environment—without interventions or full DAG modeling. It introduces a lightweight data-generation assumption, strictly weaker than standard causal discovery premises, imposing minimal distributional constraints on non-target variables. For the first time, it systematically establishes multiple identifiability conditions under the no-intervention, single-environment setting. Leveraging structural constraint theory, the authors design two robust algorithms that integrate conditional independence testing with score-based optimization within a finite-sample estimation framework. Evaluated on benchmark and real-world datasets, the proposed methods significantly outperform baselines such as ICP—achieving higher accuracy and greater robustness. This work provides both theoretically more permissive and practically more viable foundations for local causal inference.

This study investigates whether Bayesian networks can be mapped to probabilistic structural causal models (SCMs) and analyzes the implications of such a mapping for network structure and joint distributions. By introducing independent latent random variables, deterministic structural equations are extended into probabilistic form, establishing correspondences between the two frameworks at semantic, structural, and distributional levels. Leveraging tools from linear algebra and linear programming, the work formulates criteria for the existence and uniqueness of such model transformations, revealing how these conditions depend on model dimensionality. The analysis further elucidates the theoretical consequences of the transformation for causal semantics and the resulting probability distributions.

This work addresses the lack of a systematic approach to composing and ordering do-calculus rules, which hinders efficient exploration of the space of equivalent interventional queries. The paper introduces, for the first time, a derivation graph structure that formally captures the application and composition logic of do-calculus rules, systematically representing equivalence relations between observational and interventional probabilities under the do-calculus framework. Building upon this representation, the authors devise a streamlined identification procedure requiring at most four simplification steps. This approach not only reveals the intrinsic organizational structure underlying do-calculus reasoning but also enables the generation of multiple equivalent estimands for the same causal quantity, substantially improving estimation efficiency and facilitating practical applications of do-calculus.

This work addresses the challenge of providing causal explanations for rare events (outliers) by formally defining causal paths and establishing their testable conditions. Building upon structural equation models, it uniquely integrates causal paths with the theory of causal abstraction, enabling verification that relies solely on pathways relevant to the rare event rather than requiring a complete causal graph. This approach bridges the gap between intuitive causal explanations and rigorous modeling, thereby constructing a causal abstraction framework tailored to rare events and supporting formal validation of root cause analysis results.

This work addresses the challenge of causal inference in equilibrium systems confounded by latent variables, where interpretable graphical modeling approaches have been lacking. It introduces antorial graphs into the causal modeling of equilibrium systems for the first time, integrating counterfactual graphs with the Single-World Intervention Graph (SWIG) framework to construct a unified, interpretable causal diagram that jointly represents both observed and counterfactual variables. The proposed method not only yields a clear graphical representation of confounded equilibrium systems but also enables on-demand construction of covariate adjustment sets, offering element-wise flexibility to selectively include or exclude specific variables. This fine-grained control facilitates valid and efficient identification of causal effects under complex equilibrium conditions.