Organizations: Fujitsu Limited · Faculty of Data Science, Shiga University · RIKEN AIP · Computer Centre, Gakushuin University · SANKEN, The University of Osaka
Causal discovery from observational data is a fundamental tool in various fields of science. While existing approaches are typically designed for a single dataset, we often need to handle multiple datasets with non-identical variable sets in practice. One straightforward approach is to estimate a causal graph from each dataset and construct a single causal graph by overlapping. However, this approach identifies limited causal relationships because unobserved variables in each dataset can be confounders, and some variable pairs may be unobserved in any dataset. To address this issue, we leverage Causal Additive Models with Unobserved Variables (CAM-UV) that provide causal graphs having information related to unobserved variables. We show that the ground truth causal graph has structural consistency with the information of CAM-UV on each dataset. As a result, we propose an approach named I-CAM-UV to integrate CAM-UV results by enumerating all consistent causal graphs. We also provide an efficient combinatorial search algorithm and demonstrate the usefulness of I-CAM-UV against existing methods.
Figures & tables
Figure 1: Illustration of unobserved causal path (UCP) and unobserved backdoor path (UBP).
Figure 2: Example of CAM-UV. A UCP v4→v5→v6 and a UBP v2←v1→v3 are found. The dashed lines indicate undirected edges of the resulting mixed graph.
Figure 3: Example of inputs on a scenario we consider (left) and their simple overlapping (right).
Figure 4: Example of I-CAM-UV on the input of Figure 3 .
Figure 5: Example of I-CAM-UV resulting a unique DAG.
Figure 6: Examples of I-CAM-UV with relaxation.
Figure 7: Accuracies on synthetic datasets.
Figure 8: Number of DAGs enumerated by I-CAM-UV.
Figure 9: Accuracy distributions on specific instances of synthetic datasets. The heatmaps show the distributions of DAGs output by I-CAM-UV.
Figure 10: Computation times on synthetic datasets.
Appendix figures & tables12 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 11: Causal graph of fMRI dataset
Figure 12: Accuracies on fMRI dataset.
Figure 13: Number of DAGs enumerated by I-CAM-UV on fMRI dataset.
Figure 14: Accuracy distributions on specific instances of fMRI dataset. The heatmaps show the distributions of DAGs output by I-CAM-UV. The top fours are cases of b=0 , the middle fours are cases of b=1 , and the bottom fours are cases of b=2 .
Figure 15: Computation times on fMRI dataset.
Figure 16: Minimum inconsistency costs on synthetic dataset.
Figure 17: Minimum inconsistency costs on fMRI dataset.
Figure 18: Status attainment model based on domain knowledge ( Duncan et al. 1972 ) . The solid directed edges represent expected causal relationships. The dashed bi-directed edges represent not modeled causal relationships, e.g., there may be latent confounders between the two, there may be a directed edge between the two, or the two may be independent.
Figure 19: CAM-UV results for status attainment model dataset. The solid directed edges represent estimated causal relationships. The dashed edges represent not identified causal relationships due to the estimated existence of UCBs/UBPs.
Figure 20: Three examples of the graphs enumerated by I-CAM-UV with specifying “Son’s Income” becomes the sink. The solid black directed edges represent correctly estimated causal relationships. The dashed red directed edges represent wrongly estimated causal relationships. The dotted blue directed edges represent expected but not estimated causal relationships.
Figure 21: Three examples of the graphs enumerated by I-CAM-UV with specifying the following conditions: “Son’s Income” becomes the sink, and there is a causal relationship from “Father’s Education” to “Son’s Education”. The solid black directed edges represent correctly estimated causal relationships. The dashed red directed edges represent wrongly estimated causal relationships. The dotted blue directed edges represent expected but not estimated causal relationships.
Figure 22: Three examples of the graphs enumerated by I-CAM-UV with specifying the following conditions: “Son’s Income” becomes the sink, there is a causal relationship from “Father’s Education” to “Son’s Education”, and there is a causal relationship from “Father’s Occupation” to “Son’s Education”. The solid black directed edges represent correctly estimated causal relationships. The dashed red directed edges represent wrongly estimated causal relationships. The dotted blue directed edges represent expected but not estimated causal relationships.
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 F1, +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.
Patrick Blöbaum, Krishnakumar Balasubramanian, Shiva Prasad Kasiviswanathan
Amazon Web Services · Department of Statistics, University of California, Davis
Causal discovery from observational data is a fundamental yet challenging task in scientific research. While existing approaches are primarily based on conditional independence tests, structure scores, or restrictive functional assumptions, we propose Decoupled Causal Discovery (DCD), a novel decoupling-based perspective that does not rely on these methodologies. DCD directly identifies the Markov boundary (MB) by decoupling non-target variables via weighting functions, such that only variables within the MB preserve dependence with the target under the decoupled distribution. Building on this, DCD iteratively constructs the Completed Partially Directed Acyclic Graph (CPDAG) by exploiting structural asymmetries within the MBs. We establish the theoretical identifiability, soundness, and completeness of DCD. Empirical evaluations demonstrate that DCD achieves strong performance, particularly excelling in challenging noise regimes.
Zhengkang Guan, Fei Wu, Kun Kuang
College of Computer Science and Technology Zhejiang University
While causal discovery methods have matured for complete data, such algorithms for handling missing values remain limited. We establish general sufficient conditions under which causal graphs remain identifiable (i.e., uniquely determined from the available data distribution) under various missingness categories, including Missing Not At Random, and provide a framework to extend correctness guarantees from causal discovery algorithms for complete data to missing data settings. Our results show that identifiability of causal graphs with no unobserved confounders is preserved when (1) missingness mechanisms do not causally interact, (2) no variable directly causes its own missingness, and (3) either faithfulness holds for missingness mechanisms, or they follow generalized linear models. Guided by these theoretical results, we introduce two asymptotically correct algorithms for Additive Noise Models (ANMs) that recover the underlying causal graph and provide consistent parameter estimates.
Oregon State University, Causal Intelligence and Reasoning Lab, Corvallis, USA · RIKEN Advanced Intelligence Project, Causal Inference Team, Tokyo, Japan · The University of Osaka, Reasoning for Intelligence Department, Osaka, Japan +1