Knowledge-Informed Local Causal Discovery of Optimal Adjustment Sets

Discovering the direct causes and effects of a target variable from observational data is a fundamental problem in causal discovery, with broad applications in domains such as gene regulatory analysis and biomedical research. Existing causal discovery methods either learn a global causal structure, which incurs substantial computational cost, or assume the absence of latent variables and selection bias, assumptions that are often violated in real-world settings. Motivated by these challenges, we study local causal structure learning in the presence of latent variables and selection bias. Specifically, we first characterize a local region that enables target-specific causal discovery without recovering the entire global structure. We then establish a theoretical bridge between causal information learned from the observed distribution induced on this local region and the corresponding information in the global causal structure. Building on these foundations, we propose LoCaLS, a local causal structure learning algorithm that is sound and complete under standard assumptions and identifies the same direct causes and effects of a target variable as those identifiable by global causal discovery methods, while allowing for latent variables and selection bias. Extensive experiments on random and real-world structures demonstrate that the proposed method consistently achieves higher structural accuracy than existing local methods while requiring substantially less computational effort than state-of-the-art global methods. Furthermore, applications to two real-world gene expression datasets reveal biologically plausible target-specific causal structures, demonstrating its practical applicability in large-scale biological data analysis.

Expert background knowledge is often available in practical applications of causal discovery. Such constraints on the true causal graph can help causal discovery in terms of identifiability of causal effects and accuracy of the learned structure, but also in reducing the space of candidate causal graphs. As causal discovery can become computationally expensive for large number of variables, it is crucial to utilize background knowledge effectively during the causal discovery process. However, most current methods only use background knowledge in a postprocessing step after causal discovery to refine the learned graph. In this work, we develop a framework for utilizing background knowledge during the causal discovery process, focusing especially on scalable causal discovery methods that recover only a subset of the whole graph. We implement our framework for multiple algorithms and empirically show that utilizing background knowledge can both reduce computational requirements and increase the quality of the learned structures.

Causal discovery from observational data remains challenging due to the need to recover directed structure and latent confounding without interventions. We propose FoundCause, an amortized causal discovery model trained entirely on synthetic data that maps datasets directly to causal graphs in a single forward pass. By learning from large collections of simulated structural causal models, FoundCause captures transferable statistical patterns that generalize beyond individual datasets. The architecture incorporates several key inductive biases for causal discovery. It uses a permutation-invariant transformer encoder with alternating attention over samples and variables to jointly model cross-variable dependence and per-variable distributions. Pairwise statistical features derived from classical asymmetry measures are injected through statistics-conditioned attention, guiding the model toward known causal signals. A factorized decoder separates edge existence from direction, while a triangular refinement module enables reasoning over higher-order causal motifs such as chains and colliders. In addition, a dedicated confounder module based on learnable latent tokens explicitly models hidden common causes, and the model explicitly handles missing data via its masked input representation. To our knowledge, FoundCause is the first amortized causal discovery approach to explicitly model latent confounding. FoundCause outperforms 11 classical non-amortized methods (e.g., PC, GES, NOTEARS-style optimization) and 4 amortized causal discovery methods on 15 real-world datasets, achieving +9.6% improvement in $F_1$, +1.2% in AUROC, and an 18.9% reduction in structural Hamming distance relative to the strongest non-amortized methods, while performing inference in a single forward pass.