Pith. sign in

REVIEW 4 major objections 5 minor 39 references

Causal Explainability of Machine Learning in Heart Failure Prediction from Electronic Health Records

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read Replacing binary heart-failure labels with continuous MLP likelihood scores lets nonlinear causal discovery rank clinically plausible causal variables, and gradient-boosted feature importance tracks those causal strengths (Spearman 0.89)…

desk verdict An interesting application undermined by a load-bearing flaw: replacing the binary HF label with an MLP likelihood score makes the 'causal strengths' tautological, so the headline rho=0.89 is not causal evidence. read the letter →

arxiv 2506.03068 v1 pith:NZ7ZXIUL submitted 2025-06-03 stat.ML cs.CYcs.LG

Yina Hou , Shourav B. Rabbani , Liang Hong , Norou Diawara , Manar D. Samad This is my paper
classification stat.MLcs.CYcs.LG
keywords causalstructurediscoveryheartfailureelectronichealthrecordsfeatureimportancegradient-boostedtreesDirectLiNGAMNOTEARS-MLPstrength
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

This paper claims that causal structure discovery can be made to work on mixed-type electronic health record data with a binary heart-failure outcome, and that the result is clinically meaningful when the causal model is nonlinear. To do this, the authors replace the binary label with continuous MLP likelihood scores, then run DirectLiNGAM (linear) and NOTEARS-MLP (nonlinear) and compare the rank order of causal variables against feature importance from gradient-boosted trees and logistic regression, and against correlations with the likelihood score. The central empirical claim is that feature importance from gradient-boosted trees correlates closely with causal strength from the nonlinear model (Spearman 0.89 for causal variables, 0.90 for effect variables), while the linear model's correlations are weaker and often not significant. The paper also claims that correlated variables tend to be causal rather than effect variables for heart failure, and that nonlinear causal discovery correctly identifies age as the most causal factor. A sympathetic reader would care because the result suggests that importance scores from accurate ML classifiers carry causal information about the disease, giving clinicians a causal explanation for black-box predictions.

What carries the argument

The mechanism that carries the argument is the discrete-to-continuous label transformation: a multilayer perceptron trained on the binary heart-failure label produces per-sample probability scores $\hat{y} = \sigma(\mathrm{MLP}(X))$ (Equation 8), which are then concatenated with the 33 clinical features and fed into causal discovery as an ordinary continuous variable. The two causal structure discovery models then supply causal strength from their adjacency matrices: DirectLiNGAM via mutual-information-based causal ordering with linear regressions, and NOTEARS-MLP via L2 norms of first-layer MLP weights aggregated into a DAG adjacency matrix with a trace-exponential acyclicity penalty. The rank orders of these causal strengths are compared with gradient-boosted tree and logistic-regression feature importance ranks, and with Pearson correlations with the likelihood score, using Spearman correlation at $\alpha=0.05$.

What would settle it

A concrete check: generate synthetic data from a known nonlinear causal graph with a binary outcome, run the full pipeline, and compare recovered edges to the ground truth; additionally, retrain the MLP with different random seeds and see whether the edges into the score node stay fixed even though the underlying causal model is unchanged.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a continuous likelihood score produced by a multilayer perceptron can act as a stand-in for a binary disease outcome in causal structure discovery, and that the causal strengths recovered by the nonlinear NOTEARS-MLP model align with the feature-importance ranks of gradient-boosted trees at Spearman 0.89 (p<0.05) for causal variables, whereas the linear DirectLiNGAM model shows no significant correlation with ML importance for causal variables. The same pattern holds for effect variables with the nonlinear model (0.90, p<0.05). The paper further reports that variables most correlated with the likelihood score are more often causal than effect variables in the recovered DAG, and that age emerges as the top causal factor for heart failure under NOTEARS-MLP, which the authors take as evidence that the nonlinear model captures clinically plausible cause-effect structure.

Load-bearing premise

The load-bearing premise is that the MLP's predicted probability can stand in for the binary heart-failure label as an ordinary continuous variable, so that causal edges to and from that score represent the disease's true cause-and-effect relations.

Editorial extensions

If this is right

  • If the central claim is correct, feature-importance ranks from gradient-boosted trees on EHR data can be read as a first-order approximation of nonlinear causal strength, adding a causal readout to black-box classifiers without extra data collection.
  • The framework generalizes to any binary disease outcome, enabling causal discovery on diagnoses rather than only continuous biomarkers.
  • Variables that are both strongly correlated and ML-important should be expected to be causal for the disease, whereas strongly correlated variables that never appear as causes are candidates for being effects or confounded markers.
  • Linear causal discovery on such data can be misleading: it would label age and weight as effects of heart failure, reversing their clinical role.

Reading between the lines

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

  • Editorial extension: because $\hat{y}$ is a deterministic function of the input features, causal edges involving the score node may encode the MLP's learned decision boundary rather than disease biology; the reported causal strengths are at least partly predictive attributions, so the 0.89 correlation may partly reflect that both rankers use the same nonlinear signal rather than independent causal
  • Editorial extension: the paper's external check that age is the most causal factor rests on a single clinical anchor; a stronger test is to run the same pipeline on synthetic data with known structural equations and measure edge recovery, which the authors do not do.
  • Editorial extension: misclassified samples are dropped before causal discovery, so the DAG is estimated only on the easy-to-classify subpopulation; re-running with all samples or a different label proxy would test whether the reported ranks are population-wide.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper addresses whether machine-learning feature importance can serve as a causal explanation for heart failure (HF). The authors replace the binary HF label with a continuous likelihood score y_hat = sigma(MLP(X)) produced by a trained MLP, use this score as a node in DirectLiNGAM and NOTEARS-MLP causal discovery, and compare the resulting causal-strength ranks with GBT and logistic-regression importance ranks and with Pearson correlations on an All of Us EHR cohort. They report that NOTEARS-MLP causal strengths correlate strongly with GBT importance (Spearman rho = 0.89), that age is the most causal factor, and conclude that nonlinear causal structure discovery is more meaningful than linear causal structure discovery. The central technical move is Eq. (8) in Section 3.4, where the discrete outcome is replaced by a deterministic function of all input features.

Significance. Should the method work, the paper would offer a practical bridge between predictive ML and causal discovery for binary clinical outcomes, and the empirical comparison across feature types would be informative. The paper uses a real EHR cohort and reports rank correlations carefully. However, the causal interpretation fails at the central step: y_hat is a deterministic function of the input features, so the 'causal strength' scores are functions of the fitted classifier rather than estimates of independent causal mechanisms. The reported agreement between ML importance and NOTEARS-MLP causal strength is therefore expected as a comparison of two predictive attributions, not evidence for causal concordance. The manuscript also introduces a sample-selection step that further violates the assumptions of the causal discovery methods. Because these issues affect all reported causal results, the paper's central claims are not supported.

major comments (4)
  1. [§3.4, Eq. (8); §3.6.1] The transformation y_hat = sigma(MLP(X)) makes the disease node a deterministic function of all predictors. DirectLiNGAM's causal ordering is based on tests of independence between a variable and residuals from regressions on the remaining variables (Eqs. (1)-(2)); for a deterministic node those residuals are zero by construction, so the independence test is degenerate. NOTEARS-MLP (Eqs. (3)-(7)) reconstructs each variable from the others under a regression/additive-noise loss; for y_hat it can achieve near-zero reconstruction error by construction. Thus any edge X -> y_hat is a transcription of the fitted MLP rather than a discovered causal relation, and an edge y_hat -> X would state that the score (which already contains X) causes X. The assumption in Section 3.6.1 that the likelihood scores are a 'correct proxy' is unsupported and is precisely the invalid step. The causal-strength ranks in Tables 2-4 and the Spearman rho = 0.89 in Section 4.3 are predictive attributions, not causal strengths.
  2. [§3.6.1; §3.6.2] After training the MLP, the authors remove misclassified samples and use only the correctly classified subset for causal discovery and for training the GBT feature-importance model. Selection is therefore made on a variable, correct classification, that depends on both the features and the binary label and on the fitted classifier. This is a collider-like selection that can induce spurious dependencies among the remaining variables and makes the causal-discovery and feature-importance samples unrepresentative of the cohort. The manuscript does not compare with full-sample results or model the selection mechanism. Without such a check, even the predictive-rank comparisons are on a biased subset.
  3. [§5] The claim that 'NOTEARS-MLP correctly identifies age as the most causal factor for HF' is validated by appeal to medical knowledge rather than by an identified causal effect, an intervention, or a ground-truth benchmark. Agreement with a prior belief is not evidence that the discovery method recovered the true causal structure; moreover, the causal-strength scores are already, by Eq. (8), functions of the fitted MLP, so the agreement with medical consensus cannot rescue the causal interpretation.
  4. [§6; §3.4] The stated contribution of handling mixed-type (categorical, numerical, binary) variables is not demonstrated. The experimental data are continuous clinical measurements plus the binary HF label, and the only transformation is applied to the outcome. DirectLiNGAM remains a linear continuous method, and no categorical predictor enters the causal discovery. The conclusion in Section 6 that the method 'can handle both categorical and numerical variables' overstates what was implemented and tested.
minor comments (5)
  1. [§3.2] Equation (1) writes X = beta X + Gz + e, which is not a well-formed structural equation as written; beta should be defined or the notation should be revised.
  2. [§3.2] The sentence following Eq. (2) says 'for a pair of features P and Q, DirectLiNGAM will consider both possible directions: (1) P->Q and (2) Q->J'; the second direction should read Q->P.
  3. [§4.5] The final sentence of Section 4.5 ends with the isolated value '(0.89, p < 0.05)' without a clear referent; this appears to be an editing remnant.
  4. [§4.3; Table 4] The phrase 'the same strong correlation' is ambiguous because the LR correlations reported in Table 4 are 0.82, not the 0.89 reported for GBT.
  5. [Background, §2] The Peter-Clark (PC) algorithm is cited to Pearl's Causality [11], but the standard citation is Spirtes, Glymour, and Scheines; this should be corrected.

Circularity Check

3 steps flagged · score 8.0 of 10

The central causal claim reduces to a predictive concordance: the DAG's disease node is defined as σ(MLP(X)) (Eq. 8), so the 'causal strengths' encode the fitted classifier; the reported ρ = 0.89 with GBT importance compares two predictive attributions on the same samples and labels, and the claimed superiority of nonlinear CSD is built into the construction.

  1. self definitional [Section 3.4, Eq. 8; Section 3.6.1]
    "We utilize a multi-layer perceptron (MLP) to transform a discrete binary label into continuous-valued likelihood scores, enabling the discovery of causal structures between a disease and predictor variables. An MLP yields likelihood scores for a disease label given input features using a non-linear activation function. ŷ=σ(MLP(X)). (8) ... Continuous-valued likelihood scores, representing the non-linear relationship between the predictors and disease outcome, are used as a proxy for discrete class labels in subsequent causal discovery."

    In Eq. 8 the node that represents heart failure in the DAG is defined as σ(MLP(X)), a deterministic function of all predictor variables. After training, ŷ has zero residual variance given X. When this score is concatenated with X (Section 3.6.1) and fed to NOTEARS-MLP or DirectLiNGAM, edges X_j→ŷ merely re-encode the fitted classifier: NOTEARS-MLP's regressors minimize ‖ŷ − MLP(X)‖² (Eq. 7) and directly recover that function, while DirectLiNGAM's residual-independence test is degenerate for a deterministic node. The 'causal strength' of X_j for HF is therefore the sensitivity of the authors' own MLP to X_j, and edges ŷ→X_k infer disease-causes-measurement from a score already containing X_k.

  2. fitted input called prediction [Section 3.6.2; Section 4.3, Table 4]
    "In the second step, the samples correctly classified in the previous step are used to obtain feature importance scores and rank order by training a Gradient Boosting Tree (GBT) classifier. ... The causal variables of NOTEARS-MLP are strongly correlated (0.89, p <0.05) with the important variables of GBT for classification."

    Both rank sets are generated from the same filtered samples and the same binary labels. The MLP is trained on y to produce ŷ; the DAG 'causal strengths' then measure how strongly each feature predicts ŷ; the GBT is trained on y on the identical correctly-classified samples (Section 3.6.2). The Spearman ρ = 0.89 therefore compares two predictive attributions of the same X→y relationship. Since the 'causal' rank contains no information beyond a fitted predictor of the same outcome, strong concordance with GBT importance is statistically forced rather than evidence that ML-important features are causally responsible for HF. Reporting this concordance as the paper's central result is a fitted input (the MLP-derived score) presented as a validated causal prediction.

1 more flagged steps
  1. self definitional [Section 5 (Discussion)]
    "First, a non-linear causal structure discovery (e.g., NOTEARS-MLP) is more accurate and reliable than its linear counterparts (e.g., DirectLiNGAM). This superiority stems from their ability to capture non-linear relationships, addressing the limitations of linear methods. ... This statement may be validated based on standard medical knowledge that affirms age as the most causal factor in cardiovascular disorders, including HF [39]. NOTEARS-MLP correctly identifies age as the most causal factor for HF."

    The conclusion that nonlinear CSD is 'more accurate and reliable' than DirectLiNGAM is enforced by the construction itself: the disease node was deliberately defined as a nonlinear function of X (sigmoid of an MLP, Eq. 8). A nonlinear model can fit this constructed node essentially perfectly, while a linear model cannot; the comparison is therefore not evidence that nonlinear causal discovery is more meaningful in general. The Section 5 check that 'NOTEARS-MLP correctly identifies age as the most causal factor' is validated by appeal to standard medical knowledge rather than by an independently estimated causal effect, so it cannot break the definitional circularity; it merely states that the fitted attribution agrees with consensus.

full rationale

The paper's central claims — that 'causal strengths' from nonlinear CSD correlate with GBT feature importance (ρ = 0.89) and that nonlinear CSD is 'more meaningful' than linear CSD — are not independent of the paper's inputs. The disease variable is manufactured from the features (Eq. 8: ŷ = σ(MLP(X))), so edge weights involving ŷ encode the authors' own classifier; the GBT importance ranks are computed on the same samples and the same labels; and the nonlinearity injected into the target node guarantees the nonlinear method's superiority. The paper's own validation ('age is the most causal factor,' per medical consensus) is a post-hoc consistency check, not an identified causal effect, so it does not rescue the inference. DirectLiNGAM is also applied to a deterministic nonlinear node, violating its independent-noise assumption, which further undermines the asymmetrical comparison. The self-citations (Samad et al., refs [3], [4], [34]) are not load-bearing for these claims and do not affect the score. Overall, the causal interpretation reduces to predictive attribution: the inferred 'causal strengths' are inherited from the fitted MLP, and the headline concordance is between two predictive attributions of the same relationship. Hence a score of 8, indicating the central result is forced by definition rather than by a self-citation chain.

Assumptions & free parameters 4 free parameters · 3 assumptions · 1 invented entities

The ledger shows that the key input is a fitted neural network, and the core assumption is that its output can be treated as a real causal node. This assumption is not supported and is the source of the circularity. Additional selection and hyperparameter choices are not reported.

free parameters (4)
  • MLP weights (trained network) = not reported
    The likelihood scores are produced by a 4-layer MLP trained until 90% accuracy; exact weights and stopping criterion are not given, making the proxy non-reproducible.
  • Class weights w0, w1 = not reported
    Used in the loss function in Eq. 9 but values are not stated.
  • NOTEARS-MLP hyperparameters (alpha, rho, lambda) = not reported
    These control sparsity and acyclicity penalty in Eqs. 6-7 and are not specified.
  • 90% accuracy threshold = 90%
    The MLP training is stopped when 90% accuracy is reached; this arbitrary threshold affects which samples are selected for downstream analysis.
assumptions (3)
  • domain assumption The observed variables follow a DAG with independent additive noise
    Required by DirectLiNGAM and NOTEARS-MLP; not tested on this EHR data.
  • ad hoc to paper MLP likelihood scores are a valid continuous proxy for the true disease outcome in causal discovery
    This is the core enabling assumption; it is not argued from theory and conflicts with the score being a deterministic function of the features.
  • ad hoc to paper Correctly classified samples are representative of the full cohort
    Misclassified samples are removed, which changes the distribution and may bias causal and importance estimates.
invented entities (1)
  • Continuous likelihood score (MLP output)
    purpose: Serve as a continuous node for the binary HF outcome in causal discovery
    The score is a fitted function of the input features, not a measured quantity, so it has no independent causal status.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Causal Explainability of Machine Learning in Heart Failure Prediction from Electronic Health Records." pith.science (2026). https://pith.science/paper/NZ7ZXIUL

@misc{pith2026250603068,
  author       = {Pith},
  title        = {Pith review of: Causal Explainability of Machine Learning in Heart Failure Prediction from Electronic Health Records},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NZ7ZXIUL}},
  note         = {Machine review of arXiv:2506.03068}
}
read the original abstract

The importance of clinical variables in the prognosis of the disease is explained using statistical correlation or machine learning (ML). However, the predictive importance of these variables may not represent their causal relationships with diseases. This paper uses clinical variables from a heart failure (HF) patient cohort to investigate the causal explainability of important variables obtained in statistical and ML contexts. Due to inherent regression modeling, popular causal discovery methods strictly assume that the cause and effect variables are numerical and continuous. This paper proposes a new computational framework to enable causal structure discovery (CSD) and score the causal strength of mixed-type (categorical, numerical, binary) clinical variables for binary disease outcomes. In HF classification, we investigate the association between the importance rank order of three feature types: correlated features, features important for ML predictions, and causal features. Our results demonstrate that CSD modeling for nonlinear causal relationships is more meaningful than its linear counterparts. Feature importance obtained from nonlinear classifiers (e.g., gradient-boosting trees) strongly correlates with the causal strength of variables without differentiating cause and effect variables. Correlated variables can be causal for HF, but they are rarely identified as effect variables. These results can be used to add the causal explanation of variables important for ML-based prediction modeling.

Figures

Figures reproduced from arXiv: 2506.03068 by the authors.

Figure 1
Figure 1. Proposed computational framework for causal structure discovery between continuous variables and binary [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Histogram of binary {0, 1} class labels and continuous likelihood scores between 0 and 1. LDAG = αh(W(θ)) + ρ 2 |h(W)| 2 . (6) The hyperparameters α and ρ regulate the acyclicity penalty strength. Since the latter penalizes changes more heavily, its strength is halved. The loss function to optimize all MLP regressors includes three components: mean-squared loss of N regressors, L1 regularization to introduce sparsit… view at source ↗
Figure 3
Figure 3. Direct Acyclic Graph (DAG) generated by the NOTEARS-MLP model demonstrating the cause (X [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Direct Acyclic Graph (DAG) generated by the DirectLiNGAM model demonstrating the cause (X [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

39 extracted references · 32 canonical work pages

  1. [1]

    S. Yang, P. Varghese, E. Stephenson, K. Tu, J. Gronsbell, Machine learning approaches for electronic health records phenotyping: a methodical review, Journal of the American Medical Informatics Association 30 (2) (2023) 367–381

    work page 2023

  2. [2]

    S. A. Pendergrass, D. C. Crawford, Using electronic health records to generate phenotypes for research, Current protocols in human genetics 100 (1) (2019) e80

    work page 2019

  3. [3]

    M. D. Samad, A. Ulloa, G. J. Wehner, L. Jing, D. Hartzel, C. W. Good, B. A. Williams, C. M. Haggerty, B. K. Fornwalt, Predicting survival from large echocardiography and electronic health record datasets: Optimization with machine learning, JACC: Cardiovascular Imaging 12 (2019) 681–689.doi:10.1016/j.jcmg.2018.04. 026. URLhttps://linkinghub.elsevier.com/r...

    work page doi:10.1016/j.jcmg.2018.04 2019

  4. [4]

    M. D. Samad, G. J. Wehner, M. R. Arbabshirani, L. Jing, A. J. Powell, T. Geva, C. M. Haggerty, B. K. Forn- walt, Predicting deterioration of ventricular function in patients with repaired tetralogy of fallot using machine learning, European Heart Journal Cardiovascular Imaging 19 (2018) 730–738.doi:10.1093/ehjci/jey003

    work page doi:10.1093/ehjci/jey003 2018

  5. [5]

    R. Cai, J. Qiao, K. Zhang, Z. Zhang, Z. Hao, Causal discovery from discrete data using hidden compact repre- sentation, Advances in neural information processing systems 31 (2018)

    work page 2018

  6. [6]

    A. V . Bubnova, I. Deeva, A. V . Kalyuzhnaya, Mixbn: library for learning bayesian networks from mixed data, Procedia Computer Science 193 (2021) 494–503

    work page 2021

  7. [7]

    Uchida, K

    T. Uchida, K. Fujiwara, K. Nishioji, M. Kobayashi, M. Kano, Y . Seko, K. Yamaguchi, Y . Itoh, H. Kadotani, Medical checkup data analysis method based on lingam and its application to nonalcoholic fatty liver disease, Artificial intelligence in medicine 128 (2022) 102310

    work page 2022

  8. [8]

    Kotoku, A

    J. Kotoku, A. Oyama, K. Kitazumi, H. Toki, A. Haga, R. Yamamoto, M. Shinzawa, M. Yamakawa, S. Fukui, K. Yamamoto, et al., Causal relations of health indices inferred statistically using the directlingam algorithm from big data of osaka prefecture health checkups, Plos one 15 (12) (2020) e0243229

    work page 2020

Show all 39 references
  1. [9]

    N. Naik, A. Khandelwal, M. Joshi, M. Atre, H. Wright, K. Kannan, S. Hill, G. Mamidipudi, G. Srinivasa, C. Bifulco, et al., Applying large language models for causal structure learning in non small cell lung cancer, in: 2024 IEEE 12th International Conference on Healthcare Info...

    2024

  2. [10]

    P. L. Spirtes, C. Meek, T. S. Richardson, Causal inference in the presence of latent variables and selection bias, arXiv preprint arXiv:1302.4983 (2013)

    2013 arXiv

  3. [11]

    Pearl, Causality, Cambridge university press, 2009

    J. Pearl, Causality, Cambridge university press, 2009

    2009

  4. [12]

    Triantafillou, I

    S. Triantafillou, I. Tsamardinos, A. Roumpelaki, Learning neighborhoods of high confidence in constraint-based causal discovery, in: Probabilistic Graphical Models: 7th European Workshop, PGM 2014, Utrecht, The Nether- lands, September 17-19, 2014. Proceedings 7, Springer, 201...

    2014

  5. [13]

    Verny, N

    L. Verny, N. Sella, S. Affeldt, P. P. Singh, H. Isambert, Learning causal networks with latent variables from multivariate information in genomic data, PLoS computational biology 13 (10) (2017) e1005662. 10 APREPRINT- SEPTEMBER14, 2025

    2017

  6. [14]

    M. Jia, D. Y . Yuan, T. C. Lovelace, M. Hu, P. V . Benos, Causal discovery in high-dimensional, multicollinear datasets, Frontiers in epidemiology 2 (2022) 899655

    2022

  7. [15]

    Upadhyaya, K

    P. Upadhyaya, K. Zhang, C. Li, X. Jiang, Y . Kim, et al., Scalable causal structure learning: Scoping review of traditional and deep learning algorithms and new opportunities in biomedicine, JMIR Medical Informatics 11 (1) (2023) e38266

    2023

  8. [16]

    Aragam, Greedy equivalence search for nonparametric graphical models, arXiv preprint arXiv:2406.17228 (2024)

    B. Aragam, Greedy equivalence search for nonparametric graphical models, arXiv preprint arXiv:2406.17228 (2024)

    2024 arXiv

  9. [17]

    Y . Zhu, P. V . Benos, M. Chikina, A hybrid constrained continuous optimization approach for optimal causal discovery from biological data, Bioinformatics 40 (Supplement 2) (2024) ii87–ii97

    2024

  10. [18]

    Zhang, S

    K. Zhang, S. Zhu, M. Kalander, I. Ng, J. Ye, Z. Chen, L. Pan, gcastle: A python toolbox for causal discovery, arXiv preprint arXiv:2111.15155 (2021)

    2021 arXiv

  11. [19]

    Zheng, B

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

    2018

  12. [20]

    Zheng, C

    X. Zheng, C. Dan, B. Aragam, P. Ravikumar, E. Xing, Learning sparse nonparametric dags, in: International Conference on Artificial Intelligence and Statistics, Pmlr, 2020, pp. 3414–3425

    2020

  13. [21]

    D. Yang, X. He, J. Wang, G. Yu, C. Domeniconi, J. Zhang, Federated causality learning with explainable adaptive optimization, in: Proceedings of the AAAI Conference on Artificial Intelligence, V ol. 38, 2024, pp. 16308– 16315

    2024

  14. [22]

    C. Li, X. Shen, W. Pan, Nonlinear causal discovery with confounders, Journal of the American Statistical Asso- ciation 119 (546) (2024) 1205–1214

    2024

  15. [23]

    X. Shen, S. Ma, P. Vemuri, M. R. Castro, P. J. Caraballo, G. J. Simon, A novel method for causal structure discovery from ehr data, a demonstration on type-2 diabetes mellitus, arXiv preprint arXiv:2011.05489 (2020)

    2020 arXiv

  16. [24]

    Shimizu, P

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

    2006

  17. [25]

    Shimizu, A

    S. Shimizu, A. Hyvarinen, Y . Kawahara, A direct method for estimating a causal ordering in a linear non-gaussian acyclic model, arXiv preprint arXiv:1408.2038 (2014)

    2014 arXiv

  18. [26]

    M. Cai, H. Hara, Learning causal graphs using variable grouping according to ancestral relationship, arXiv preprint arXiv:2403.14125 (2024)

    2024

  19. [27]

    Shimizu, T

    S. Shimizu, T. Inazumi, Y . Sogawa, A. Hyvarinen, Y . Kawahara, T. Washio, P. O. Hoyer, K. Bollen, P. Hoyer, Directlingam: A direct method for learning a linear non-gaussian structural equation model, Journal of Machine Learning Research-JMLR 12 (Apr) (2011) 1225–1248

    2011

  20. [28]

    Glymour, K

    C. Glymour, K. Zhang, P. Spirtes, Review of causal discovery methods based on graphical models, Frontiers in genetics 10 (2019) 524

    2019

  21. [29]

    O. C. Mesner, Non-parametric causal discovery for discrete and continuous data, Ph.D. thesis, Carnegie Mellon University (2020)

    2020

  22. [30]

    Zanga, E

    A. Zanga, E. Ozkirimli, F. Stella, A survey on causal discovery: theory and practice, International Journal of Approximate Reasoning 151 (2022) 101–129

    2022

  23. [31]

    Y . Li, R. Xia, C. Liu, L. Sun, A hybrid causal structure learning algorithm for mixed-type data, in: Proceedings of the AAAI Conference on Artificial Intelligence, V ol. 36, 2022, pp. 7435–7443

    2022

  24. [32]

    Y . Zhao, J. Jia, Notears-m: Causal bayesian network structure learning of mixed type data and its application in identifying disease risk factors (2024)

    2024

  25. [33]

    Rashid, J

    R. Rashid, J. Chowdhury, G. Terejanu, Causal feature selection: Methods and a novel causal metric evaluation framework, in: 2023 IEEE 10th International Conference on Data Science and Advanced Analytics (DSAA), IEEE, 2023, pp. 1–9. 11 APREPRINT- SEPTEMBER14, 2025

    2023

  26. [34]

    M. D. Samad, L. Jing, A. E. U. Cerna, D. N. Hartzel, B. A. Williams, C. W. Good, S. Doddamani, C. M. Haggerty, B. K. Fornwalt, Machine learning significantly improves accuracy to predict survival over the seattle heart failure model, Circulation 138 (2018) A12513–A12513

    2018

  27. [35]

    J. Wang, J. Luo, M. Ye, X. Wang, Y . Zhong, A. Chang, G. Huang, Z. Yin, C. Xiao, J. Sun, et al., Recent advances in predictive modeling with electronic health records, arXiv preprint arXiv:2402.01077 (2024)

    2024 arXiv

  28. [36]

    Huang, M

    Y . Huang, M. Kleindessner, A. Munishkin, D. Varshney, P. Guo, J. Wang, Benchmarking of data-driven causality discovery approaches in the interactions of arctic sea ice and atmosphere, Frontiers in big Data 4 (2021) 642182

    2021

  29. [37]

    of Us Research Program Investigators, J

    A. of Us Research Program Investigators, J. C. Denny, J. L. Rutter, D. B. Goldstein, A. Philippakis, J. W. Smoller, G. Jenkins, E. Dishman, The ”all of us” research program, New England Journal of Medicine 381 (2019) 668– 676.doi:10.1056/NEJMsr1809937

    2019 doi

  30. [38]

    C. W. Tsao, A. W. Aday, Z. I. Almarzooq, C. A. Anderson, P. Arora, C. L. Avery, C. M. Baker-Smith, A. Z. Beaton, A. K. Boehme, A. E. Buxton, et al., Heart disease and stroke statistics—2023 update: a report from the american heart association, Circulation 147 (8) (2023) e93–e621

    2023

  31. [39]

    H. Li, M. H. Hastings, J. Rhee, L. E. Trager, J. D. Roh, A. Rosenzweig, Targeting age-related pathways in heart failure, Circulation research 126 (4) (2020) 533–551. 12

    2020

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.