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arxiv: 2605.03045 · v1 · submitted 2026-05-04 · 💻 cs.LG

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TCD-Arena: Assessing Robustness of Time Series Causal Discovery Methods Against Assumption Violations

Gideon Stein, Joachim Denzler, Niklas Penzel, Tristan Piater

Pith reviewed 2026-05-08 18:56 UTC · model grok-4.3

classification 💻 cs.LG
keywords causal discoverytime seriesrobustnessassumption violationstesting frameworkensemblessynthetic dataempirical evaluation
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The pith

TCD-Arena is a modular testing kit that measures how time series causal discovery algorithms hold up when their assumptions are progressively violated.

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

The paper introduces TCD-Arena as a customizable toolkit for evaluating time series causal discovery methods against controlled increases in assumption violations. An empirical evaluation involving roughly 30 million individual runs produces detailed robustness profiles for 33 separate violations. The results also indicate that ensembles of multiple algorithms can deliver stronger overall performance under these conditions. The framework is intended to support development of causal discovery techniques that remain reliable across a wider range of data settings.

Core claim

We present TCD-Arena, a modularized, highly customizable, and extendable testing kit to assess the robustness of time series CD algorithms against stepwise more severe assumption violations. For demonstration, we conduct an extensive empirical study comprising around 30 million individual CD attempts and reveal nuanced robustness profiles for 33 distinct assumption violations. Further, we investigate CD ensembles and find that they have the potential to improve general robustness, which has implications for real-world applications.

What carries the argument

TCD-Arena, a modular testing kit that creates synthetic time series data with stepwise, controlled violations of standard assumptions and applies quantitative performance metrics to compare algorithms.

If this is right

  • Individual causal discovery methods exhibit distinct robustness profiles when subjected to the same set of assumption violations.
  • Some assumption violations produce larger performance losses than others, varying by algorithm.
  • Ensembles that combine several causal discovery algorithms can achieve higher robustness than any single method alone.
  • The modular design of the toolkit makes it straightforward to add new algorithms or violation types for further testing.
  • The evaluation results can inform practical selection of methods for applications where particular assumption violations are likely.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Practitioners could consult the reported robustness profiles when matching a causal discovery method to the expected characteristics of their data.
  • Algorithm developers might focus improvement efforts on the violation types that cause the largest observed drops.
  • Running TCD-Arena on real datasets alongside the synthetic tests would test whether the controlled violations predict actual performance.
  • The approach supplies a template for creating standardized benchmarks that emphasize robustness rather than performance on clean data alone.

Load-bearing premise

The 33 controlled synthetic assumption violations and the chosen performance metrics accurately represent the types and impacts of assumption violations that occur in real-world time series data.

What would settle it

Direct experiments on real time series datasets that contain documented assumption violations, showing error patterns or robustness rankings that differ markedly from the patterns produced by TCD-Arena simulations.

Figures

Figures reproduced from arXiv: 2605.03045 by Gideon Stein, Joachim Denzler, Niklas Penzel, Tristan Piater.

Figure 1
Figure 1. Figure 1: Robustness profile for GLWCG and GINST and for ten Causal Discovery algorithms against a multitude of stepwise more severe assumption violations. We measure robustness as the average normalized SHD over various data regimes and violation levels. See view at source ↗
Figure 2
Figure 2. Figure 2: Details for violation types Vobs and Vnl. Left: Observational noise violations. Right: Functional distributions that we deploy to sample fi,d,l used in Eq. (2). (2023a); Ferdous et al. (2025), a pertinent question arises: How robust are certain CD methods against different severities of assumption violation? This question is critical in applied settings. For instance, the mere existence of observational no… view at source ↗
Figure 3
Figure 3. Figure 3: Left: Average robustness of the best hyperparameter configuration per CD method and per view at source ↗
Figure 4
Figure 4. Figure 4: The experimental protocol was used to create robustness profiles for various Causal view at source ↗
Figure 5
Figure 5. Figure 5: Various depictions of different violations of observational noise. We depict the severity of view at source ↗
Figure 6
Figure 6. Figure 6: Graphical depictions of different violations and their intensities. view at source ↗
Figure 7
Figure 7. Figure 7: Graphical depictions of different violations and their intensities. view at source ↗
Figure 8
Figure 8. Figure 8: Graphical depictions of different violations and their intensities. view at source ↗
Figure 9
Figure 9. Figure 9: Graphical depictions of different violations and their intensities. view at source ↗
Figure 10
Figure 10. Figure 10: Graphical depictions of different violations and their intensities. view at source ↗
Figure 11
Figure 11. Figure 11: Depiction of problematic relationships between violation property and robustness measured view at source ↗
Figure 12
Figure 12. Figure 12: The two structures, we enforce to violate faithfulness. Note that in Fig. 12b, some of view at source ↗
Figure 13
Figure 13. Figure 13: Examples of f1, f2, and f3 with randomly sampled β from the respective level ℓ. We also visualize the optimal line and denote the corresponding parameters. Now to determine whether DMSE is smooth with respect to changes in β, we have to consider the three terms in Eq. (13) that are functions of β: fj , a ∗ , and b ∗ , where the last two also depend on the specific function fj (Eq. (12), Eq. (26)). For all… view at source ↗
Figure 14
Figure 14. Figure 14: Nonlinearity measured with DMSE for the three functions f1, f2, and f3 for increasing values of β > 0. B.4.4 2. B-SPLINES FOLLOWING A TREND: Next, we investigate univariate functions f that exhibit an overall increasing trend but are not neces￾sarily monotonic. To do this, we rely on B-spline interpolations, e.g, de Boor (2001). Specifically, we sample sample NP scalar values (interpolation points) {v1, v… view at source ↗
Figure 15
Figure 15. Figure 15: Nonlinearity measured with DMSE for the spline functions for an increasing number of interpolation points. We report the average and the standard deviations. Number of Inter- Efspline [DMSE(fspline)] polation Points 25 0.003792 15 0.006517 10 0.010198 6 0.017728 4 0.019475 view at source ↗
Figure 16
Figure 16. Figure 16: The densities of the two non-Gaussian distributions, we employ to violate standard normal view at source ↗
Figure 17
Figure 17. Figure 17: Robustness profile for GLSG and of ten Causal Discovery algorithms against a multitude of stepwise assumption violations measured as average normalized SHD over various data regimes. D.1 ADDITIONAL METRICS To extend our empirical evaluation, we include alternative metrics and additional depictions. First, we include additional depictions of the main metric (normalized minimum SHD) in view at source ↗
Figure 18
Figure 18. Figure 18: Alternative depiction 1 of robustness profiles of ten Causal Discovery algorithms against a view at source ↗
Figure 19
Figure 19. Figure 19: Alternative depiction 2 of robustness profiles of ten Causal Discovery algorithms against a view at source ↗
Figure 20
Figure 20. Figure 20: Robustness profiles of ten Causal Discovery algorithms against a multitude of stepwise view at source ↗
Figure 21
Figure 21. Figure 21: Additional depictions of the robustness profiles of ten Causal Discovery algorithms against view at source ↗
Figure 22
Figure 22. Figure 22: Robustness profiles of ten Causal Discovery algorithms against a multitude of stepwise view at source ↗
Figure 23
Figure 23. Figure 23: Additional depictions of the robustness profiles of ten Causal Discovery algorithms against view at source ↗
Figure 24
Figure 24. Figure 24: Robustness profiles of ten Causal Discovery algorithms against a multitude of stepwise view at source ↗
Figure 25
Figure 25. Figure 25: Additional depictions of the robustness profiles of ten Causal Discovery algorithms against view at source ↗
Figure 26
Figure 26. Figure 26: Robustness profiles of ten Causal Discovery algorithms against a multitude of stepwise view at source ↗
Figure 27
Figure 27. Figure 27: Depictions of robustness profiles of ten CD algorithms against assumption violations view at source ↗
Figure 28
Figure 28. Figure 28: Robustness profiles of ten Causal Discovery algorithms against a multitude of stepwise view at source ↗
Figure 29
Figure 29. Figure 29: Depictions of robustness profiles of ten CD algorithms against assumption violations view at source ↗
Figure 33
Figure 33. Figure 33: Notably, because Causal Pretraining does not require specifying a max lag, its performance view at source ↗
Figure 30
Figure 30. Figure 30: Robustness profiles of ten Causal Discovery algorithms against a multitude of stepwise view at source ↗
Figure 31
Figure 31. Figure 31: Depictions of robustness profiles of ten CD algorithms against assumption violations view at source ↗
Figure 32
Figure 32. Figure 32: Robustness profiles of ten Causal Discovery algorithms against a multitude of stepwise view at source ↗
Figure 33
Figure 33. Figure 33: Depictions of robustness profiles of ten CD algorithms against assumption violations view at source ↗
Figure 34
Figure 34. Figure 34: Robustness improvements in comparison to the performance of Cross Correlation per view at source ↗
Figure 35
Figure 35. Figure 35: Robustness improvements in comparison to the performance of Cross Correlation per view at source ↗
Figure 36
Figure 36. Figure 36: Robustness improvements in comparison to the performance of Cross Correlation per view at source ↗
Figure 37
Figure 37. Figure 37: Performance differences (measured as normalized SHD) when uncovering the LWCG view at source ↗
Figure 38
Figure 38. Figure 38: Performance differences when uncovering the LWCG depending on hyperparameter view at source ↗
Figure 39
Figure 39. Figure 39: Performance differences (measured as normalized SHD) when uncovering the LWCG view at source ↗
Figure 40
Figure 40. Figure 40: Performance differences (measured as normalized SHD) when uncovering INST depending view at source ↗
Figure 41
Figure 41. Figure 41: Performance differences (measured as normalized SHD) when uncovering INST depending view at source ↗
read the original abstract

Causal Discovery (CD) is a powerful framework for scientific inquiry. Yet, its practical adoption is hindered by a reliance on strong, often unverifiable assumptions and a lack of robust performance assessment. To address these limitations and advance empirical CD evaluation, we present TCD-Arena, a modularized, highly customizable, and extendable testing kit to assess the robustness of time series CD algorithms against stepwise more severe assumption violations. For demonstration, we conduct an extensive empirical study comprising around 30 million individual CD attempts and reveal nuanced robustness profiles for 33 distinct assumption violations. Further, we investigate CD ensembles and find that they have the potential to improve general robustness, which has implications for real-world applications. With this, we strive to ultimately facilitate the development of CD methods that are reliable for a diverse range of synthetic and potentially real-world data conditions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript presents TCD-Arena, a modular, customizable, and extendable testing kit for assessing the robustness of time series causal discovery (CD) algorithms against 33 controlled assumption violations. Through an extensive empirical study of approximately 30 million CD attempts, it reports nuanced robustness profiles across methods and finds that CD ensembles have the potential to improve general robustness, with implications for real-world applications.

Significance. If the synthetic violation generators faithfully isolate each assumption and the chosen metrics track practical utility, this benchmark addresses a key gap in empirical CD evaluation by enabling systematic robustness testing. The modular design, scale of the experiments (~30M runs), provision of reproducible code, and ablation tables isolating single violations are clear strengths that could guide development of more reliable CD methods.

major comments (2)
  1. [Section 4.2] Section 4.2 (Data Generation and Violation Implementation): The paper supplies explicit parameterization and ablation tables for the 33 violations, but lacks quantitative verification (e.g., pre/post-violation statistical tests on unaffected properties such as stationarity or noise distribution) that each generator isolates its target without side effects. This is load-bearing for the central claim of 'nuanced robustness profiles' under stepwise severity.
  2. [Section 5.3] Section 5.3 (Ensemble Results): The claim that ensembles improve general robustness is supported by the experiments, but the aggregation procedure (e.g., voting, averaging, or selection) and whether gains are uniform across all 33 violations versus concentrated in a subset are not fully detailed; this weakens the generalizability of the ensemble recommendation.
minor comments (3)
  1. [Abstract] Abstract: Replace the approximate 'around 30 million' with the exact total count and a brief breakdown by violation category for precision and transparency.
  2. [Figure 3] Figure 3 (Robustness Profile Plots): Add error bars or confidence intervals to the performance curves to convey variability across the large number of runs.
  3. [Section 6] Section 6 (Discussion): The real-world implications paragraph would be strengthened by one concrete example linking a specific robustness profile to an application domain (e.g., finance or neuroscience time series).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and the recommendation for minor revision. We address each major comment point-by-point below and have revised the manuscript to incorporate the suggested clarifications and additions.

read point-by-point responses

  1. Referee: [Section 4.2] Section 4.2 (Data Generation and Violation Implementation): The paper supplies explicit parameterization and ablation tables for the 33 violations, but lacks quantitative verification (e.g., pre/post-violation statistical tests on unaffected properties such as stationarity or noise distribution) that each generator isolates its target without side effects. This is load-bearing for the central claim of 'nuanced robustness profiles' under stepwise severity.

    Authors: We appreciate the referee highlighting the value of explicit isolation verification. While the ablation tables and parameterization already demonstrate targeted impacts, we agree that quantitative pre/post statistical checks on non-targeted properties would further substantiate the generators' specificity. In the revised manuscript, we have added such verification to Section 4.2 (and the appendix), including Augmented Dickey-Fuller tests for stationarity and Kolmogorov-Smirnov tests for distributional properties on unaffected variables across representative violations. These confirm minimal side effects, directly supporting the reported nuanced robustness profiles. revision: yes

  2. Referee: [Section 5.3] Section 5.3 (Ensemble Results): The claim that ensembles improve general robustness is supported by the experiments, but the aggregation procedure (e.g., voting, averaging, or selection) and whether gains are uniform across all 33 violations versus concentrated in a subset are not fully detailed; this weakens the generalizability of the ensemble recommendation.

    Authors: We thank the referee for noting the need for greater detail on the ensemble procedure and its scope. In the revised Section 5.3, we have fully specified the aggregation method (majority voting on causal edge presence across the base methods). We have also added a per-violation breakdown (new table and accompanying text) showing that robustness gains occur across 29 of the 33 violations, with larger improvements for noise-related and non-stationarity violations and more modest gains elsewhere. This provides a balanced view of generalizability while highlighting where ensembles are most beneficial. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper introduces an empirical benchmark (TCD-Arena) for testing time-series causal discovery algorithms under controlled assumption violations. It contains no mathematical derivations, parameter fits, or predictions that reduce to inputs by construction. All headline claims rest on the outcomes of ~30 million reproducible simulation runs with explicitly parameterized violation generators; no self-citation chain or ansatz is required to support the reported robustness profiles or ensemble observations. The work is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the domain assumption that synthetic data with controlled violations can stand in for real-world data conditions and that the selected 33 violations plus the evaluation metrics capture the relevant robustness dimensions.

axioms (1)
  • domain assumption Time series causal discovery methods rely on strong assumptions that are often violated in practice
    Explicitly stated in the abstract as the core limitation the toolkit addresses

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Works this paper leans on

298 extracted references · 191 canonical work pages · 6 internal anchors

  1. [1]

    doi:10.1002/aisy.202400181 , abstract =

    Advanced Intelligent Systems , author =. doi:10.1002/aisy.202400181 , abstract =

    work page doi:10.1002/aisy.202400181

  2. [2]

    An introduction to causal inference , journal =

    Scheines, Richard , year =. An introduction to causal inference , journal =

  3. [3]

    Advances in neural information processing systems , author =

  4. [4]

    Efficient and

    Li, Xiu-Chuan and Liu, Tongliang , month = oct, year =. Efficient and. Proceedings of the

  5. [5]

    Proceedings of the

    Cheng, Yuxiao and Yang, Runzhao and Xiao, Tingxiong and Li, Zongren and Suo, Jinli and He, Kunlun and Dai, Qionghai , month = sep, year =. Proceedings of the

  6. [6]

    Neal, Brady and Huang, Chin-Wei and Raghupathi, Sunand , month = may, year =

  7. [7]

    Proceedings of the

    Cheng, Yuxiao and Wang, Ziqian and Xiao, Tingxiong and Zhong, Qin and Suo, Jinli and He, Kunlun , month = oct, year =. Proceedings of the

  8. [8]

    Montagna, Francesco and Noceti, Nicoletta and Rosasco, Lorenzo and Zhang, Kun and Locatello, Francesco , month = mar, year =. Causal. Proceedings of the 2nd

  9. [9]

    Shirali, Ali and Abebe, Rediet and Hardt, Moritz , month = sep, year =. A. Proceedings of the

  10. [10]

    , month = oct, year =

    Zhang, Jiji and Spirtes, Peter L. , month = oct, year =. Strong. doi:10.48550/arXiv.1212.2506 , abstract =

    work page doi:10.48550/arxiv.1212.2506

  11. [11]

    2025 , pages =

    Proceedings of the AAAI Conference on Artificial Intelligence , author =. 2025 , pages =. doi:10.1609/aaai.v39i18.34136 , abstract =

    work page doi:10.1609/aaai.v39i18.34136 2025

  12. [12]

    Günther, Wiebke and Ninad, Urmi and Runge, Jakob , month = jul, year =. Causal. Proceedings of the

  13. [13]

    and Devijver, Emilie and Gaussier, Eric , month = aug, year =

    Assaad, Charles K. and Devijver, Emilie and Gaussier, Eric , month = aug, year =. Discovery of extended summary graphs in time series , url =. Proceedings of the

  14. [14]

    High-recall causal discovery for autocorrelated time series with latent confounders , volume =

    Gerhardus, Andreas and Runge, Jakob , year =. High-recall causal discovery for autocorrelated time series with latent confounders , volume =. Advances in

  15. [15]

    Enhancing

    Castri, Luca and Mghames, Sariah and Hanheide, Marc and Bellotto, Nicola , month = aug, year =. Enhancing. Proceedings of the

  16. [16]

    Butterworth, Stephen. On. Scribd , publisher =. 1930 , pages =

    1930

  17. [17]

    Koukounas, Andreas and Mastrapas, Georgios and Günther, Michael and Wang, Bo and Martens, Scott and Mohr, Isabelle and Sturua, Saba and Akram, Mohammad Kalim and Martínez, Joan Fontanals and Ognawala, Saahil and Guzman, Susana and Werk, Maximilian and Wang, Nan and Xiao, Han , month = jun, year =. Jina. doi:10.48550/arXiv.2405.20204 , abstract =

    work page doi:10.48550/arxiv.2405.20204

  18. [18]

    IEEE Transactions on Pattern Analysis and Machine Intelligence , author =

    Addressing. IEEE Transactions on Pattern Analysis and Machine Intelligence , author =. 2025 , keywords =. doi:10.1109/TPAMI.2025.3553957 , abstract =

    work page doi:10.1109/tpami.2025.3553957 2025

  19. [19]

    and Wahl, Jonas and Ninad, Urmi and Runge, Jakob , month = may, year =

    Herman, Rebecca J. and Wahl, Jonas and Ninad, Urmi and Runge, Jakob , month = may, year =. Unitless. doi:10.48550/arXiv.2503.17037 , abstract =

    work page doi:10.48550/arxiv.2503.17037

  20. [20]

    ACM Comput

    Deep. ACM Comput. Surv. , author =. 2025 , pages =. doi:10.1145/3762179 , abstract =

    work page doi:10.1145/3762179 2025

  21. [21]

    Results in Engineering , author =

    A systematic review of monocular depth estimation for autonomous driving:. Results in Engineering , author =. 2025 , keywords =. doi:10.1016/j.rineng.2025.105359 , abstract =

    work page doi:10.1016/j.rineng.2025.105359 2025

  22. [22]

    ACM Comput

    Deep. ACM Comput. Surv. , author =. 2024 , pages =. doi:10.1145/3677327 , abstract =

    work page doi:10.1145/3677327 2024

  23. [23]

    , month = jul, year =

    Jyothi Unni, Suraj and Sheth, Paras and Ding, Kaize and Liu, Huan and Selcuk Candan, K. , month = jul, year =. doi:10.48550/arXiv.2307.13757 , abstract =

    work page doi:10.48550/arxiv.2307.13757

  24. [24]

    doi:10.48550/arXiv.2411.06391 , abstract =

    Li, Shuqi and Sun, Yuebo and Lin, Yuxin and Gao, Xin and Shang, Shuo and Yan, Rui , month = nov, year =. doi:10.48550/arXiv.2411.06391 , abstract =

    work page doi:10.48550/arxiv.2411.06391

  25. [25]

    Kumar, Nischal Ashok and Feng, Wanyong and Lee, Jaewook and McNichols, Hunter and Ghosh, Aritra and Lan, Andrew , year =. A. doi:10.5281/zenodo.8115727 , language =

    work page doi:10.5281/zenodo.8115727

  26. [26]

    Transactions on Machine Learning Research , author =

    Neural. Transactions on Machine Learning Research , author =

  27. [27]

    Advances in Neural Information Processing Systems , author =

    Amortized. Advances in Neural Information Processing Systems , author =. 2022 , pages =

    2022

  28. [28]

    Demystifying amortized causal discovery with transformers , url =

    Montagna, Francesco and Cairney-Leeming, Max and Sridhar, Dhanya and Locatello, Francesco , month = oct, year =. Demystifying amortized causal discovery with transformers , url =

  29. [29]

    Balazadeh, Vahid , month = dec, year =. vdblm/

  30. [30]

    Multimodal alignment and fusion: A survey.arXiv preprint arXiv:2411.17040, 2024

    Li, Songtao and Tang, Hao , month = oct, year =. Multimodal. doi:10.48550/arXiv.2411.17040 , abstract =

    work page doi:10.48550/arxiv.2411.17040

  31. [31]

    Karris, Nicholas and Durell, Luke and Flores, Javier and Emerson, Tegan , month = nov, year =. Which. doi:10.48550/arXiv.2511.12757 , abstract =

    work page doi:10.48550/arxiv.2511.12757

  32. [32]

    Olko, Mateusz and Gajewski, Mateusz and Wojciechowska, Joanna and Kuciński, Łukasz and Morzy, Mikołaj and Sankowski, Piotr and Miłoś, Piotr , month = oct, year =. Since

  33. [33]

    Yi, Huiyang and He, Yanyan and Chen, Duxin and Kang, Mingyu and Wang, He and Yu, Wenwu , year =. The. The

  34. [34]

    Standardizing

    Ormaniec, Weronika and Sussex, Scott and Lorch, Lars and Schölkopf, Bernhard and Krause, Andreas , year =. Standardizing. The

  35. [35]

    2021 , keywords =

    Technological Forecasting and Social Change , author =. 2021 , keywords =. doi:10.1016/j.techfore.2021.121092 , abstract =

    work page doi:10.1016/j.techfore.2021.121092 2021

  36. [36]

    Dhir, Anish and Ashman, Matthew and Requeima, James and Wilk, Mark van der , month = mar, year =. A. doi:10.48550/arXiv.2412.16577 , abstract =

    work page doi:10.48550/arxiv.2412.16577

  37. [37]

    Journal of Economic Perspectives , author =

    The. Journal of Economic Perspectives , author =. 2017 , keywords =. doi:10.1257/jep.31.2.33 , abstract =

    work page doi:10.1257/jep.31.2.33 2017

  38. [38]

    Annual Review of Sociology , author =

    Structural. Annual Review of Sociology , author =. 1977 , pages =

    1977

  39. [39]

    2018 , journal =

    An overview of structural equation modeling: its beginnings, historical development, usefulness and controversies in the social sciences , volume =. Quality & Quantity , author =. 2018 , keywords =. doi:10.1007/s11135-017-0469-8 , abstract =

    work page doi:10.1007/s11135-017-0469-8 2018

  40. [40]

    and Rhemtulla, Mijke and de Vlaming, Ronald and Ritchie, Stuart J

    Genomic structural equation modelling provides insights into the multivariate genetic architecture of complex traits , volume =. Nature Human Behaviour , author =. 2019 , keywords =. doi:10.1038/s41562-019-0566-x , abstract =

    work page doi:10.1038/s41562-019-0566-x 2019

  41. [41]

    Annals of Translational Medicine , author =

    Structural equation modeling in the context of clinical research , volume =. Annals of Translational Medicine , author =. 2017 , pmid =. doi:10.21037/atm.2016.09.25 , abstract =

    work page doi:10.21037/atm.2016.09.25 2017

  42. [42]

    Bentler, P. M. , editor =. Causal. Handbook of. 1988 , doi =

    1988

  43. [43]

    and Pearl, Judea , editor =

    Bollen, Kenneth A. and Pearl, Judea , editor =. Eight. Handbook of. 2013 , doi =

    2013

  44. [44]

    1998 , title =

    Graphs,. Sociological Methods & Research , author =. 1998 , pages =. doi:10.1177/0049124198027002004 , abstract =

    work page doi:10.1177/0049124198027002004 1998

  45. [45]

    Pedobiologia , author =

    From patterns to causal understanding:. Pedobiologia , author =. 2015 , keywords =. doi:10.1016/j.pedobi.2015.03.002 , abstract =

    work page doi:10.1016/j.pedobi.2015.03.002 2015

  46. [46]

    and Hult, G

    Hair, Joseph F. and Hult, G. Tomas M. and Ringle, Christian M. and Sarstedt, Marko and Danks, Nicholas P. and Ray, Soumya , editor =. An. Partial. 2021 , doi =

    2021

  47. [47]

    Methods in Molecular Biology (Clifton, N.J.) , author =

    Structural. Methods in Molecular Biology (Clifton, N.J.) , author =. 2017 , pmid =. doi:10.1007/978-1-4939-7274-6_28 , abstract =

    work page doi:10.1007/978-1-4939-7274-6_28 2017

  48. [48]

    Behmanesh, Maysam and Turan, Erkan and Ovsjanikov, Maks , month = sep, year =. Graph. doi:10.48550/arXiv.2509.09597 , abstract =

    work page doi:10.48550/arxiv.2509.09597

  49. [49]

    Causal discovery for time series with latent confounders , url =

    Reiser, Christian , month = sep, year =. Causal discovery for time series with latent confounders , url =. doi:10.48550/arXiv.2209.03427 , abstract =

    work page doi:10.48550/arxiv.2209.03427

  50. [50]

    Learning Transferable Visual Models From Natural Language Supervision

    Radford, Alec and Kim, Jong Wook and Hallacy, Chris and Ramesh, Aditya and Goh, Gabriel and Agarwal, Sandhini and Sastry, Girish and Askell, Amanda and Mishkin, Pamela and Clark, Jack and Krueger, Gretchen and Sutskever, Ilya , month = feb, year =. Learning. doi:10.48550/arXiv.2103.00020 , abstract =

    work page internal anchor Pith review doi:10.48550/arxiv.2103.00020

  51. [51]

    Proceedings of the 31st

    Ferdous, Muhammad Hasan and Hossain, Emam and Gani, Md Osman , month = aug, year =. Proceedings of the 31st. doi:10.1145/3711896.3737439 , abstract =

    work page doi:10.1145/3711896.3737439

  52. [52]

    IEEE Transactions on Image Processing , author =

    Practical. IEEE Transactions on Image Processing , author =. 2014 , keywords =. doi:10.1109/TIP.2014.2347204 , abstract =

    work page doi:10.1109/tip.2014.2347204 2014

  53. [53]

    The American Statistician , author =

    Distinguishing “. The American Statistician , author =. 1996 , pages =. doi:10.1080/00031305.1996.10474381 , number =

    work page doi:10.1080/00031305.1996.10474381 1996

  54. [54]

    McKendrick

    A contribution to the mathematical theory of epidemics , volume =. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character , author =. 1997 , pages =. doi:10.1098/rspa.1927.0118 , abstract =

    work page doi:10.1098/rspa.1927.0118 1997

  55. [55]

    A contribution to the mathematical theory of epidemics

  56. [56]

    Hydrology and Earth System Sciences , author =

    A high-resolution dataset of water fluxes and states for. Hydrology and Earth System Sciences , author =. 2017 , pages =. doi:10.5194/hess-21-1769-2017 , abstract =

    work page doi:10.5194/hess-21-1769-2017 2017

  57. [57]

    CausalDynamics: A large-scale benchmark for structural discovery of dynamical causal models

    Herdeanu, Benjamin and Nathaniel, Juan and Roesch, Carla and Buch, Jatan and Ramien, Gregor and Haux, Johannes and Gentine, Pierre , month = may, year =. doi:10.48550/arXiv.2505.16620 , abstract =

    work page doi:10.48550/arxiv.2505.16620

  58. [58]

    Position:

    Poinsot, Audrey and Panayiotou, Panayiotis and Leite, Alessandro and Chesneau, Nicolas and Şimşek, Özgür and Schoenauer, Marc , month = jun, year =. Position:

  59. [59]

    IEEE Transactions on Image Processing , author =

    Practical. IEEE Transactions on Image Processing , author =. 2008 , keywords =. doi:10.1109/TIP.2008.2001399 , abstract =

    work page doi:10.1109/tip.2008.2001399 2008

  60. [60]

    Philosophy of Science , author =

    When to. Philosophy of Science , author =. 2013 , pages =. doi:10.1086/673937 , number =

    work page doi:10.1086/673937 2013

  61. [61]

    Psychology Science , author =

    The robustness of parametric statistical methods , volume =. Psychology Science , author =. 2004 , pages =

    2004

  62. [62]

    Chaos , author =

    Causal network reconstruction from time series:. Chaos: An Interdisciplinary Journal of Nonlinear Science , author =. 2018 , pages =. doi:10.1063/1.5025050 , abstract =

    work page doi:10.1063/1.5025050 2018

  63. [63]

    Statistical Science , author =

    Bayesian. Statistical Science , author =. 2024 , keywords =. doi:10.1214/23-STS905 , abstract =

    work page doi:10.1214/23-sts905 2024

  64. [64]

    2016 , title =

    Causal discovery and inference: concepts and recent methodological advances , volume =. Applied Informatics , author =. 2016 , keywords =. doi:10.1186/s40535-016-0018-x , abstract =

    work page doi:10.1186/s40535-016-0018-x 2016

  65. [65]

    and Aisen, Paul and Petersen, Ronald and Jack, Clifford R

    Challenges and. Scientific Reports , author =. 2020 , keywords =. doi:10.1038/s41598-020-59669-x , abstract =

    work page doi:10.1038/s41598-020-59669-x 2020

  66. [66]

    Biometrika , author =

    Identifiability of. Biometrika , author =. 2014 , pages =. doi:10.1093/biomet/ast043 , abstract =

    work page doi:10.1093/biomet/ast043 2014

  67. [67]

    Advances in Neural Information Processing Systems , author =

    Conditional. Advances in Neural Information Processing Systems , author =. 2022 , pages =

    2022

  68. [68]

    , editor =

    Stone, Lewi and Katriel, Guy and Hilker, Frank M. , editor =. Encyclopedia of. 2012 , pages =

    2012

  69. [69]

    Michaelis-

    Ainsworth, Stanley , editor =. Michaelis-. Steady-. 1977 , doi =

    1977

  70. [70]

    Journal of Physics E: Scientific Instruments , author =

    Temperature sensor characteristics and measurement system design , volume =. Journal of Physics E: Scientific Instruments , author =. 1984 , pages =. doi:10.1088/0022-3735/17/6/002 , abstract =

    work page doi:10.1088/0022-3735/17/6/002 1984

  71. [71]

    CEUR workshop proceedings , author =

    Measurement. CEUR workshop proceedings , author =. 2016 , pmid =

    2016

  72. [72]

    The Annals of Statistics , author =

    A characterization of. The Annals of Statistics , author =. 1997 , keywords =. doi:10.1214/aos/1031833662 , abstract =

    work page doi:10.1214/aos/1031833662 1997

  73. [73]

    Bayesian Analysis , author =

    Learning. Bayesian Analysis , author =. 2018 , keywords =. doi:10.1214/18-BA1101 , abstract =

    work page doi:10.1214/18-ba1101 2018

  74. [74]

    IEEE Access , author =

    A. IEEE Access , author =. 2022 , keywords =. doi:10.1109/ACCESS.2022.3207287 , abstract =

    work page doi:10.1109/access.2022.3207287 2022

  75. [75]

    Advances in Neural Information Processing Systems , author =

    Ensemble of. Advances in Neural Information Processing Systems , author =. 2022 , pages =

    2022

  76. [76]

    and Ibeling, Duligur and Icard, Thomas , month = mar, year =

    Bareinboim, Elias and Correa, Juan D. and Ibeling, Duligur and Icard, Thomas , month = mar, year =. On. Probabilistic and

  77. [77]

    Herdeanu, Benjamin and Nathaniel, Juan and Roesch, Carla and Buch, Jatan and Ramien, Gregor and Haux, Johannes and Gentine, Pierre , month = may, year =

  78. [78]

    Frontiers in Genetics , author =

    Review of. Frontiers in Genetics , author =. 2019 , keywords =. doi:10.3389/fgene.2019.00524 , abstract =

    work page doi:10.3389/fgene.2019.00524 2019

  79. [79]

    Nonlinear

    Wu, Tianhao and Wu, Xingyu and Wang, Xin and Liu, Shikang and Chen, Huanhuan , month = oct, year =. Nonlinear. Proceedings of the 31st. doi:10.1145/3511808.3557660 , abstract =

    work page doi:10.1145/3511808.3557660

  80. [80]

    Monti, Ricardo Pio and Zhang, Kun and Hyvärinen, Aapo , month = aug, year =. Causal. Proceedings of

Showing first 80 references.