parametric causal graphs

This work addresses the high computational complexity of causal effect estimation in relational domains by introducing lifted inference to causal reasoning for the first time. It proposes the Parametrized Causal Factor Graph (PCFG) and its partially directed extension (PD-PCFG), along with the Lifted Causal Inference (LCI) algorithm. By structurally modeling intervention semantics, the approach enables efficient and exact inference even under incomplete causal knowledge. Compared to traditional propositional-level causal Bayesian networks, LCI achieves substantial gains in computational efficiency within relational settings while preserving inference accuracy.

This paper addresses the identification of conditional causal effects under maximal partially directed acyclic graphs (MPDAGs)—the equivalence class of causal DAGs over observed variables induced by background knowledge. To overcome the limitation that standard do-calculus cannot be directly applied to MPDAGs, we establish a graphical criterion for identifying adjustment sets that remain valid under intervention, thereby systematically extending do-calculus to the MPDAG framework. We further develop the first complete algorithm that determines whether an arbitrary conditional causal effect is identifiable given an MPDAG and, if so, constructs an unbiased estimand. Our approach significantly enhances the applicability and accuracy of causal inference under incomplete structural knowledge—such as partial ancestral constraints or forbidden edges—thereby providing both theoretical foundations and computational tools for robust, domain-knowledge-integrated causal analysis.

This work addresses the identifiability of causal graphs under mixed discrete/continuous variables and causal effects influencing variance or tail behavior—e.g., heteroscedastic noise or heavy-tailed distributions. We propose the Conditional Parameterized Causal Model (CPCM), which relaxes the conventional additive noise assumption and accommodates flexible distribution families, including Gaussian, Poisson, and Pareto. Crucially, we establish the first rigorous identifiability theory for causal graphs under non-additive noise. Leveraging sufficient statistics, we develop a unified theoretical framework for identifiability proof and design an efficient causal structure learning algorithm. Empirical evaluation across diverse benchmark datasets demonstrates that our method significantly improves causal discovery accuracy in settings with mixed variable types and heteroscedastic noise, achieving state-of-the-art performance.

This paper addresses high-order causal structure learning by extending the Causal Additive Model (CAM) to an additive framework that accommodates higher-order interactions. Methodologically, it introduces **Directed Acyclic Hypergraphs (DAGHs)** to model multivariate cooperative causal mechanisms, rigorously defines their Markov property and equivalence classes, and proves identifiability under strengthened assumptions—achieving unique recovery with reduced sample complexity. An enhanced greedy algorithm is designed to navigate the hypergraph search space, balancing computational feasibility and statistical consistency. Experiments on synthetic data demonstrate that the proposed DAGH-based approach significantly outperforms conventional DAG-based methods in accuracy and robustness for discovering high-order causal interactions, especially under limited sample sizes.

This work addresses the challenge of jointly learning causal structure and causal effects from observational data while providing unified support for both interventional and counterfactual queries within Pearl’s causal hierarchy. To this end, the authors propose TabPFN-CFM, the first causal foundation model based on the TabPFN architecture, which leverages synthetic data pretraining and multitask learning to simultaneously perform causal graph discovery, interventional effect estimation, and counterfactual reasoning. The model also effectively incorporates known prior structural information when available. Experimental results demonstrate that TabPFN-CFM significantly outperforms existing baselines in both causal structure learning and outcome prediction on real-world datasets, exhibiting strong generalization capabilities and superior overall performance.

This study addresses the challenge of identifying direct causal effects among observed variables in densely confounded linear structural equation models with latent variables, where conventional methods often fail. The authors propose a novel identification criterion that explicitly models latent variables, employs a recursive identification strategy, and systematically handles unidentified causal parents. By transforming the combinatorial search problem into an efficient network flow computation, the method substantially enhances the identifiability of direct causal effects in dense confounding settings. Accompanied by an open-source algorithmic implementation, this approach combines theoretical rigor with practical utility for causal inference in complex observational data.

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.