Pith. sign in

REVIEW 5 major objections 6 minor 44 references

From Observations to Causations: A GNN-based Probabilistic Prediction Framework for Causal Discovery

T0 review · 5 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A graph neural network trained once on synthetic data can predict the causal graph of a new observational dataset in a single forward pass, returning edge probabilities rather than a single deterministic structure.

desk verdict A plausible amortized GNN causal discovery pipeline, but the paper's central 'superior performance' claim is contradicted by its own Table 1. read the letter →

arxiv 2507.20349 v1 pith:V3N5CZYL submitted 2025-07-27 cs.LG stat.ME

Rezaur Rashid , Gabriel Terejanu This is my paper · ORCID
classification cs.LGstat.ME
keywords causaldiscoverygraphneuralnetworkdirectedacyclicprobabilisticinferencesupervisededgeclassificationstructuralequationmodelsSAGEpairs
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper's central claim is that causal discovery can be recast as a supervised edge-classification problem. A graph neural network, trained once on synthetic graphs generated from nonlinear structural equation models, takes the observed variables of a new dataset and outputs a probability for every ordered pair of variables being cause, effect, or unrelated. Because the output is a distribution over graphs rather than a single graph, the model carries uncertainty information, and acyclicity can be imposed afterward via topological ordering. The paper reports that this trained-once model matches or beats classical and recent optimization-based causal discovery methods on synthetic data, on the CSuite benchmarks, and on the Sachs protein-signaling data without retraining. A reader would care because it replaces per-dataset combinatorial or continuous search with a single fast prediction.

What carries the argument

Central object: a GraphSAGE-style message-passing model extended to consume edge features, acting as an edge classifier. Each node is initialized with 13 statistical features; each edge with 114 features that condense pairwise dependence, including mutual information, conditional entropy, polynomial-fit error, Pearson correlation, HSIC, and a prior edge-direction distribution from a causal-pairs model. Message passing concatenates source, target, and edge features, averages the messages over neighbors, and updates node embeddings; the final per-edge probability comes from a function f([h_i, h_j, e_ij]). A secondary mechanism is the four inference strategies (PG, MLG, PDAG, MLDAG) that convert edge probabilities into graphs, with the DAG variants using a maximum spanning DAG plus topological sorting to enforce acyclicity.

What would settle it

Hold out a real dataset whose true causal graph is known but whose data were produced by a very different mechanism than the synthetic generator, such as discrete variables, heavy measurement noise, or latent confounders; run the trained model and per-dataset baselines on it. If the model's advantage in SHD and true-positive rate disappears or reverses, the paper's generalization claim is falsified.

Watch

Extended reading notes

Core claim

The paper argues that the structural equations underlying a causal system leave measurable footprints in the joint distribution of the observed variables, and that those footprints are enough for a graph neural network to classify edge direction and existence directly. Concretely, it constructs a fully connected graph over variables, decorates each node with 13 distributional features and each edge with 114 statistical and information-theoretic features, then learns a function from concatenated node and edge embeddings to the probability of the edge being forward, reverse, or absent. Under the paper's four inference strategies, these edge probabilities form a full distribution over digraphs, or are refined into maximum-likelihood DAGs by conditioning on a topological order from a maximum spanning DAG. The reported results place the DAG-refined variants, GNN-PDAG and GNN-MLDAG, ahead of the baselines on most synthetic and CSuite comparisons and competitive on the Sachs network.

Load-bearing premise

The whole transfer rests on the assumption that the synthetic data generator used for training, with its specific graph sizes, edge densities, and sample sizes, produces statistical footprints representative enough of real-world causal systems that a model trained on it keeps its accuracy on unseen real data.

Editorial extensions

If this is right

  • Once trained, the model returns edge probabilities for a new dataset in a single forward pass, removing the need for per-dataset optimization or conditional-independence testing.
  • Acyclicity is handled downstream rather than during optimization, which lets the same learned edge probabilities serve both general digraph queries and strict DAG estimates.
  • The probabilistic output makes uncertainty quantification available to downstream users, who can sample graphs or rank edges by confidence.
  • The method scales to at least 100 nodes in training, and its reported advantage grows on denser graphs, pointing to a scalable route for complex causal systems.
  • Because the same architecture produces all four inference variants, practitioners can trade off precision against recall without retraining.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The edge-probability output could be calibrated and used as a prior for interventional or counterfactual reasoning, but the paper does not test this downstream use.
  • A natural stress test is to train the same architecture on a deliberately shifted synthetic distribution, such as different SEM families, discrete variables, or latent confounders, and measure the change in SHD; the paper only reports one training distribution.
  • Because the feature list is explicit and fixed, the framework could double as a probe for which statistical signatures actually drive causal direction, connecting to interpretability without any architectural change.
  • The reported insensitivity to data standardization suggests the model relies on scale-invariant features, a property that could be verified by ablating the moment- and variance-based edge features.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 6 minor

Summary. The paper proposes a supervised graph neural network framework for causal discovery. A fully connected graph is built over the observed variables; each node is given 13 statistical features and each edge 114 statistical, information-theoretic, and causal-pairs features. A GraphSAGE-style message-passing model with edge features is trained on synthetic graphs to classify every pair as forward edge, reverse edge, or no edge. Four inference strategies (PG, MLG, PDAG, MLDAG) from the authors' earlier work turn these edge probabilities into graphs or DAGs. The framework is evaluated without per-dataset retraining on synthetic ER and Scale-Free graphs, five CSuite benchmarks, and the Sachs protein network, and compared against PC, GES, LiNGAM, DAG-GNN, NOTEARS-MLP, DiBS, and DAGMA. The abstract claims superior accuracy and scalability over all these methods.

Significance. If the claims were supported, the contribution would be practically valuable: a single model that amortizes causal discovery, provides probabilistic outputs, and avoids per-dataset optimization. The paper is commendably concrete about its feature set, training distribution, and backbone, which makes the method reproducible in principle, and it evaluates on a broad set of standard baselines. The core empirical claim, however, is not supported by the paper's own Table 1, and the real-world evaluation is not yet rigorous enough to establish generalization. The significance is therefore conditional on a substantial revision that either demonstrates superiority in well-defined settings or reframes the contribution as a competitive amortized alternative.

major comments (5)
  1. [Section 4.3, Table 1, and abstract] The central claim of 'superior performance' is contradicted by the paper's own table. On Erdos-Renyi graphs, NOTEARS achieves SHD/d = 1.33 +/- 0.10 and TPR = 0.58 +/- 0.02, while GNN-MLDAG achieves SHD/d = 1.66 +/- 0.15 and TPR = 0.54 +/- 0.03; on Scale-Free graphs, DAGMA achieves SHD/d = 1.39 +/- 0.09 and TPR = 0.54 +/- 0.02 versus GNN-MLDAG's 1.40 +/- 0.11 and 0.48 +/- 0.03, and NOTEARS has lower SHD/d (1.36 +/- 0.11). Because the paper defines lower SHD and higher TPR as better, these numbers show that the proposed GNN variants are not consistently superior even under in-distribution synthetic data. The abstract, Section 1, and the first paragraph of Section 4.3 need to be rewritten, or the authors need paired per-graph statistical tests that identify the specific settings in which the GNN methods beat the baselines.
  2. [Sections 3.1 and 3.3] The novelty claim is confounded with self-reference. Three of the 114 edge features are the causal-pairs direction probabilities from the authors' own Rashid et al. (2022), and the inference procedures PG, MLG, PDAG, and MLDAG (Eqs. 5-10) are explicitly taken from that same paper, with the reader referred there for 'detailed algorithmic derivations and proofs.' The evaluation then compares the GNN framework against CausalPairs as if it were an independent baseline. The comparison to CausalPairs is best understood as an ablation of the GNN aggregation layer, not as a comparison against an unrelated method; this should be stated explicitly, and the paper should delineate which components are new.
  3. [Section 4.3, Tables 2 and 3] The real-world evidence is not sufficient to support the claimed generalization. Table 2 reports one SHD/d, TPR, and FPR value per dataset with no repeated runs or error bars; Table 3 switches to Predicted/Correct/Reversed edge counts, a different metric family, and for non-standardized data the DAG-GNN and NOTEARS-MLP results are quoted from their original manuscripts rather than produced under the same pipeline. The conclusion that the model 'effectively generalizes to real-world datasets' is therefore not supported by the tables as they stand. The authors should add repeated runs with matched preprocessing, report consistent metrics, and document the distribution shift between training and test.
  4. [Section 3.3, Eq. 9] The maximum likelihood topological ordering used by PDAG and MLDAG is approximated as the topological sort of the maximum spanning DAG of the edge-probability graph, and no analysis or empirical check of this approximation is provided. Since PDAG/MLDAG are the variants highlighted as the best performers, this step is load-bearing; the paper should either supply a proof or a direct comparison with a search-based ordering, or explicitly report the sensitivity of the final DAG to this approximation.
  5. [Section 4.1] The synthetic test data in Table 1 come from the same generative family as the training data (graph models ER/SF, d in {10,20,50,100}, edge ratios {1d,2d,4d}, sample sizes {500,1000,2000}, nonlinear SEMs 'similar to the NOTEARS-MLP implementation'), so Table 1 only demonstrates interpolation in distribution. The headline generalization to CSuite and Sachs is an out-of-distribution claim, but Tables 2 and 3 are the only evidence and, as noted above, are not yet adequate. Please add held-out synthetic families, larger-d or different-n test cases, or otherwise restrict the generalization claim.
minor comments (6)
  1. [Equation 1] The symbol e_ij is overloaded: it denotes both the categorical edge label (values -1, 0, 1) and the edge feature vector, making the conditioning in p(e_ij | h_i, h_j, e_ij) confusing; use different symbols (e.g., y_ij for the label and x_ij for the feature vector).
  2. [Section 4.1] The list of CSuite datasets ends with 'symprod simpson (4 nodes, 4 edges);.'; remove the stray semicolon or period.
  3. [Section 3.1 and Appendix] The text says the full feature list is in 'Appendix 5,' but the appendix is unnumbered; reference it properly (e.g., Appendix A) and include a table that explicitly sums the 114 edge features, since the current grouped list does not make the count verifiable.
  4. [Figure 2] The figure uses 'Normalized TPR,' 'Normalized FPR,' and 'Normalized SHD/d' without defining the normalization; define it in the caption so the reader can interpret the magnitudes.
  5. [Table 2 caption] The phrase 'trained on synthetic train data' is redundant; use 'trained on synthetic data.'
  6. [General] The paper does not include a data or code availability statement; providing the trained model and generation scripts would materially improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the GNN is trained on external ground truth, and the cited CausalPairs component is an input feature and inference routine, not the predicted output.

full rationale

The paper's central claim is that a GNN trained once on synthetic graphs predicts edge probabilities and hence causal structures on new data. The training labels are external ground-truth graphs, and the evaluations on CSuite and Sachs are out-of-sample benchmarks with no per-dataset fitting. The main self-references are: (i) three of the 114 edge features come from the authors' CausalPairs model (Rashid et al., 2022), and (ii) the four inference procedures PG/MLG/PDAG/MLDAG are taken from the same prior work. Neither creates definitional circularity. The CausalPairs probability is an input feature, not the output: the GNN must learn a nonlinear function of 114 features plus node embeddings and is supervised by ground-truth edge labels, so its prediction is not equal to the CausalPairs feature by construction. The inference equations (5)-(10) are fully stated in the paper, so citing Rashid et al. for derivations is not load-bearing. The comparison against CausalPairs baselines is a comparison against a stripped-down version of a component, which is a legitimate ablation-style baseline rather than a circular derivation. The correctness question raised by Table 1 (NOTEARS and DAGMA matching or beating the proposed methods on synthetic SHD/TPR) is an internal-evidence conflict with the abstract's 'superior performance' claim, but it is a correctness risk, not a circularity. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported, and no known result is repackaged as new. The paper is self-contained against external benchmarks, so the circularity score is 0.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The framework contributes a learned edge classifier on top of a largely hand-designed feature set and an inference layer taken from the authors' prior work. The only genuinely new fitted component is the GNN's learned weights and hyperparameters; the feature set and the probabilistic inference machinery are imported, and the central accuracy claim depends on the unproven representativeness of the synthetic training distribution.

free parameters (2)
  • GNN architecture hyperparameters = not reported
    Number of layers, hidden dimensions, learning rate, epochs, and neighbor sampling are chosen by hand and never listed; they directly determine the reported accuracy but cannot be checked or reproduced from the paper.
  • CausalPairs edge-direction probabilities (3 values per edge) = trained in prior work (Rashid et al., 2022)
    These are used as edge features and are the outputs of a classifier trained on data in the authors' earlier paper; the current paper's performance depends on the quality of these features, but their training details are not given here.
assumptions (5)
  • domain assumption Observations are i.i.d. samples from a distribution consistent with the underlying DAG
    Stated in Section 3: 'Assuming we have n i.i.d. observations in the data matrix X.' Causal discovery from observational data requires faithfulness or similar assumptions, which are not discussed.
  • domain assumption The true causal structure is acyclic (a DAG)
    The PDAG and MLDAG inference enforces acyclicity; if the generating process contains feedback cycles, the DAG-constrained outputs are misspecified.
  • ad hoc to paper Edge directions are conditionally independent given the node and edge features (Eq. 5)
    The graph probability factorizes as a product over edge probabilities; any correlations between edges are ignored. This approximation is inherited from Rashid et al. (2022) and is used to compute PG and MLG.
  • ad hoc to paper The maximum spanning DAG's topological ordering approximates the true order (Eq. 9)
    Used to approximate p(G | DAG); if the MSDAG ordering is incorrect, the DAG-constrained probabilities and MLDAG output are mis-specified.
  • ad hoc to paper The 114 edge features, including CausalPairs probabilities, are sufficient to identify causal direction for the test distributions
    No identifiability theory is given; the method's accuracy rests on the empirical assumption that the feature set separates cause from effect in the test data. This is the core inductive bias of the supervised approach.

how reviews work

0 comments
Cite this review

Pith. "Pith review of From Observations to Causations: A GNN-based Probabilistic Prediction Framework for Causal Discovery." pith.science (2026). https://pith.science/paper/V3N5CZYL

@misc{pith2026250720349,
  author       = {Pith},
  title        = {Pith review of: From Observations to Causations: A GNN-based Probabilistic Prediction Framework for Causal Discovery},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V3N5CZYL}},
  note         = {Machine review of arXiv:2507.20349}
}
read the original abstract

Causal discovery from observational data is challenging, especially with large datasets and complex relationships. Traditional methods often struggle with scalability and capturing global structural information. To overcome these limitations, we introduce a novel graph neural network (GNN)-based probabilistic framework that learns a probability distribution over the entire space of causal graphs, unlike methods that output a single deterministic graph. Our framework leverages a GNN that encodes both node and edge attributes into a unified graph representation, enabling the model to learn complex causal structures directly from data. The GNN model is trained on a diverse set of synthetic datasets augmented with statistical and information-theoretic measures, such as mutual information and conditional entropy, capturing both local and global data properties. We frame causal discovery as a supervised learning problem, directly predicting the entire graph structure. Our approach demonstrates superior performance, outperforming both traditional and recent non-GNN-based methods, as well as a GNN-based approach, in terms of accuracy and scalability on synthetic and real-world datasets without further training. This probabilistic framework significantly improves causal structure learning, with broad implications for decision-making and scientific discovery across various fields.

Figures

Figures reproduced from arXiv: 2507.20349 by the authors.

Figure 1
Figure 1. Schematic of the proposed framework. Each node is initialized with statistical features, and each edge with ag [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Comparison of normalized Structural Hamming Distance (SHD/d), True Positive Rate (TPR), and False Positive [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Performance comparison between GNN-based methods and CausalPairs methods on smaller CSuite datasets: (a) [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

44 extracted references · 26 canonical work pages

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry add.period write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.state := if if FUNCTION not #0 #1 if FUNCTION and 'skip pop #0 if FUNCTIO...

  2. [2]

    and Wang, B

    Behnam, A. and Wang, B. (2024). Graph neural network causal explanation via neural causal models. In European Conference on Computer Vision , pages 410--427. Springer

    work page 2024

  3. [3]

    Bello, K., Aragam, B., and Ravikumar, P. (2022). DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization . In Advances in Neural Information Processing Systems

    work page 2022

  4. [4]

    Bouckaert, R. R. (1993). Probabilistic network construction using the minimum description length principle. In European conference on symbolic and quantitative approaches to reasoning and uncertainty , pages 41--48. Springer

    work page 1993

  5. [5]

    Brouillard, P., Lachapelle, S., Lacoste, A., Lacoste-Julien, S., and Drouin, A. (2020). Differentiable causal discovery from interventional data. Advances in Neural Information Processing Systems , 33:21865--21877

    work page 2020

  6. [6]

    Chickering, D. M. (2002). Optimal structure identification with greedy search. Journal of machine learning research , 3(Nov):507--554

    2002

  7. [7]

    Fonollosa, J. A. (2019). Conditional distribution variability measures for causality detection. Cause Effect Pairs in Machine Learning , pages 339--347

    work page 2019

  8. [8]

    A., Mateo, J

    G \'a mez, J. A., Mateo, J. L., and Puerta, J. M. (2011). Learning bayesian networks by hill climbing: efficient methods based on progressive restriction of the neighborhood. Data Mining and Knowledge Discovery , 22:106--148

    work page 2011

Show all 44 references
  1. [9]

    Gao, H., Yao, C., Li, J., Si, L., Jin, Y., Wu, F., Zheng, C., and Liu, H. (2024). Rethinking causal relationships learning in graph neural networks. In Proceedings of the AAAI Conference on Artificial Intelligence , volume 38, pages 12145--12154

    2024

  2. [10]

    Geffner, T., Antoran, J., Foster, A., Gong, W., Ma, C., Kiciman, E., Sharma, A., Lamb, A., Kukla, M., Pawlowski, N., Allamanis, M., and Zhang, C. (2022). Deep end-to-end causal inference. arXiv preprint arXiv:2202.02195

    2022 arXiv

  3. [11]

    Hamilton, W., Ying, Z., and Leskovec, J. (2017). Inductive representation learning on large graphs. Advances in neural information processing systems , 30

    2017

  4. [12]

    Heckerman, D., Geiger, D., and Chickering, D. M. (1995). Learning bayesian networks: The combination of knowledge and statistical data. Machine learning , 20:197--243

    1995

  5. [13]

    Jiang, W., Liu, H., and Xiong, H. (2023). When graph neural network meets causality: Opportunities, methodologies and an outlook. arXiv preprint arXiv:2312.12477

    2023 arXiv

  6. [14]

    Job, S., Tao, X., Cai, T., Xie, H., Li, L., Li, Q., and Yong, J. (2025). Exploring causal learning through graph neural networks: An in-depth review. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery , 15(2):e70024

    2025

  7. [15]

    Kipf, T. N. and Welling, M. (2016). Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907

    2016 arXiv

  8. [16]

    and Friedman, N

    Koller, D. and Friedman, N. (2009). Probabilistic graphical models: principles and techniques . MIT press

    2009

  9. [17]

    L., Ramsey, J., and Hoyer, P

    Lacerda, G., Spirtes, P. L., Ramsey, J., and Hoyer, P. O. (2012). Discovering cyclic causal models by independent components analysis. arXiv preprint arXiv:1206.3273

    2012 arXiv

  10. [18]

    Li, H., Xiao, Q., and Tian, J. (2020). Supervised whole dag causal discovery. arXiv preprint arXiv:2006.04697

    2020 arXiv

  11. [19]

    Lin, W., Lan, H., and Li, B. (2021). Generative causal explanations for graph neural networks. In International Conference on Machine Learning , pages 6666--6679. PMLR

    2021

  12. [20]

    Lorch, L., Rothfuss, J., Sch \"o lkopf, B., and Krause, A. (2021). Dibs: Differentiable bayesian structure learning. Advances in Neural Information Processing Systems , 34

    2021

  13. [21]

    Lorch, L., Sussex, S., Rothfuss, J., Krause, A., and Sch \"o lkopf, B. (2022). Amortized inference for causal structure learning. Advances in Neural Information Processing Systems , 35:13104--13118

    2022

  14. [22]

    and Pereira, F

    McDonald, R. and Pereira, F. (2006). Online learning of approximate dependency parsing algorithms. In 11th Conference of the European Chapter of the Association for Computational Linguistics , pages 81--88

    2006

  15. [23]

    and Wit, E

    Mohammadi, A. and Wit, E. C. (2015). Bayesian structure learning in sparse gaussian graphical models

    2015

  16. [24]

    Mohan, K., Chung, M., Han, S., Witten, D., Lee, S.-I., and Fazel, M. (2012). Structured learning of gaussian graphical models. Advances in neural information processing systems , 25

    2012

  17. [25]

    Ng, I., Zhu, S., Chen, Z., and Fang, Z. (2019). A graph autoencoder approach to causal structure learning. arXiv preprint arXiv:1911.07420

    2019 arXiv

  18. [26]

    Ott, S., Imoto, S., and Miyano, S. (2003). Finding optimal models for small gene networks. In Biocomputing 2004 , pages 557--567. World Scientific

    2003

  19. [27]

    Pearl, J. (2019). The seven tools of causal inference, with reflections on machine learning. Communications of the ACM , 62(3):54--60

    2019

  20. [28]

    Peters, J., Janzing, D., and Sch \"o lkopf, B. (2017). Elements of causal inference: foundations and learning algorithms . The MIT Press

    2017

  21. [29]

    Rashid, R., Chowdhury, J., and Terejanu, G. (2022). From causal pairs to causal graphs. In 2022 21st IEEE International Conference on Machine Learning and Applications (ICMLA) , pages 802--807. IEEE

    2022

  22. [30]

    Reisach, A., Seiler, C., and Weichwald, S. (2021). Beware of the simulated dag! causal discovery benchmarks may be easy to game. Advances in Neural Information Processing Systems , 34:27772--27784

    2021

  23. [31]

    A., and Nolan, G

    Sachs, K., Perez, O., Pe'er, D., Lauffenburger, D. A., and Nolan, G. P. (2005). Causal protein-signaling networks derived from multiparameter single-cell data. Science , 308(5721):523--529

    2005

  24. [32]

    Schluter, N. (2014). On maximum spanning dag algorithms for semantic dag parsing. In Proceedings of the ACL 2014 Workshop on Semantic Parsing , pages 61--65

    2014

  25. [33]

    O., Hyv \"a rinen, A., Kerminen, A., and Jordan, M

    Shimizu, S., Hoyer, P. O., Hyv \"a rinen, A., Kerminen, A., and Jordan, M. (2006). A linear non-gaussian acyclic model for causal discovery. Journal of Machine Learning Research , 7(10)

    2006

  26. [34]

    Singh, K., Gupta, G., Vig, L., Shroff, G., and Agarwal, P. (2017). Deep convolutional neural networks for pairwise causality. arXiv preprint arXiv:1701.00597

    2017 arXiv

  27. [35]

    Spirtes, P., Glymour, C., and Scheines, R. (2001). Causation, prediction, and search . MIT press

    2001

  28. [36]

    E., and Aliferis, C

    Tsamardinos, I., Brown, L. E., and Aliferis, C. F. (2006). The max-min hill-climbing bayesian network structure learning algorithm. Machine learning , 65:31--78

    2006

  29. [37]

    Velickovic, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y., et al. (2017). Graph attention networks. stat , 1050(20):10--48550

    2017

  30. [38]

    and Patgiri, R

    Waikhom, L. and Patgiri, R. (2023). A survey of graph neural networks in various learning paradigms: methods, applications, and challenges. Artificial Intelligence Review , 56(7):6295--6364

    2023

  31. [39]

    Yu, Y., Chen, J., Gao, T., and Yu, M. (2019). Dag-gnn: Dag structure learning with graph neural networks. In International Conference on Machine Learning , pages 7154--7163. PMLR

    2019

  32. [40]

    S., Veli c kovi \'c , P., and Kersting, K

    Ze c evi \'c , M., Dhami, D. S., Veli c kovi \'c , P., and Kersting, K. (2021). Relating graph neural networks to structural causal models. arXiv preprint arXiv:2109.04173

    2021 arXiv

  33. [41]

    Zhao, S., Prapas, I., Karasante, I., Xiong, Z., Papoutsis, I., Camps-Valls, G., and Zhu, X. X. (2024). Causal graph neural networks for wildfire danger prediction. arXiv preprint arXiv:2403.08414

    2024 arXiv

  34. [42]

    K., and Xing, E

    Zheng, X., Aragam, B., Ravikumar, P. K., and Xing, E. P. (2018). Dags with no tears: Continuous optimization for structure learning. Advances in neural information processing systems , 31

    2018

  35. [43]

    Zheng, X., Dan, C., Aragam, B., Ravikumar, P., and Xing, E. (2020). Learning sparse nonparametric dags. In International Conference on Artificial Intelligence and Statistics , pages 3414--3425. Pmlr

    2020

  36. [44]

    Zhou, J., Cui, G., Hu, S., Zhang, Z., Yang, C., Liu, Z., Wang, L., Li, C., and Sun, M. (2020). Graph neural networks: A review of methods and applications. AI open , 1:57--81

    2020

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.