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arxiv: 2408.02679 · v3 · submitted 2024-07-31 · 💻 cs.LG · cs.GR· cs.HC· stat.ME

Visual Analysis of Multi-outcome Causal Graphs

Pith reviewed 2026-05-23 22:40 UTC · model grok-4.3

classification 💻 cs.LG cs.GRcs.HCstat.ME
keywords visual analysiscausal graphsmulti-outcome causal graphscausal discoverycomparative visualizationhealthcare visualizationmultimorbidity
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The pith

A visual analysis method lets analysts build and compare causal graphs tied to different outcome variables.

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

The paper introduces a visual analysis approach designed for multi-outcome causal graphs, collections of causal graphs each linked to a separate outcome variable. This setup matters in healthcare because it helps examine multimorbidity and comorbidity by revealing how causes overlap or differ across outcomes. Two techniques were created with medical experts: a progressive visualization that compares causal discovery algorithms on mixed continuous and categorical data to refine single-outcome graphs, and a comparative graph layout with custom visual encodings to spot differences and shared elements across graphs. The workflow starts with building separate graphs for each outcome and then applies the comparative tools to the resulting multi-outcome set. Evaluations on benchmark data, a medical case study, and expert user studies with real health datasets test the approach.

Core claim

The paper establishes a visual analysis method for multi-outcome causal graphs in which analysts first construct individual causal graphs for each outcome variable using a progressive visualization that compares multiple causal discovery algorithms on mixed-type data, then generate and display the collection of graphs through a comparative layout and specialized encodings to examine their differences and commonalities.

What carries the argument

The comparative graph layout technique together with specialized visual encodings that support quick side-by-side inspection of multiple causal graphs for differences and commonalities.

If this is right

  • Analysts can refine a single-outcome causal graph by progressively comparing outputs from multiple discovery algorithms on mixed continuous and categorical datasets.
  • Individual outcome graphs can be assembled into a multi-outcome collection and examined together for shared and unique causal relations.
  • The method extends to real-world health research data as demonstrated in the case study and expert evaluations.

Where Pith is reading between the lines

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

  • The same layout and encoding choices could be tested on causal graphs from domains other than healthcare, such as economics or environmental science.
  • Integrating the progressive algorithm comparison step directly into interactive graph editing might reduce the number of manual refinements needed.
  • Scalability tests on datasets with dozens of outcomes would show whether the comparative layout remains readable as the number of graphs grows.

Load-bearing premise

The two comparative visualization techniques developed with expert input effectively support quick comparison of differences and commonalities across multi-outcome causal graphs.

What would settle it

A user study in which medical experts fail to identify causal differences or commonalities faster or more accurately with the new comparative layout than with ordinary side-by-side graph views would falsify the claim of effective support.

Figures

Figures reproduced from arXiv: 2408.02679 by Daniel Weiskopf, Huai-Yu Wang, Jinlu Yu, Liang Zhou, Mengjie Fan, Nan Cao.

Figure 1
Figure 1. Figure 1: The overall process of the visual analysis of multi-outcome causal graphs of a health research dataset [ [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The workflow of our visual analysis method. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Visualization of the true causal graphs (left column) and results of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The user interface of our visual analysis system for single outcome graphs consists of three views: (1) Dataset and Variables Selection View [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Visualization of multi-outcome causal graphs with our new layout and visual mappings. Numbers on top of each subgraph are the horizontal [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Visual mappings for comparison of multi-outcome causal graphs. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The case study of UKB data with a medical expert. Single causal graph analysis (1–4) and multi-outcome causal graphs comparison (5, 6). [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Visualization of multi-outcome causal graphs with (a) subgraphs extracted directly from the supergraph and (b) our new comparable graph layout. [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The overall process of the visual analysis of multi-outcome causal graphs of a health research data [ [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: The case study of UKB data with a medical expert. Single causal graph analysis (1–4) and multi-outcome causal graphs comparison (5, 6). [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
read the original abstract

We introduce a visual analysis method for multiple causal graphs with different outcome variables, namely, multi-outcome causal graphs. Multi-outcome causal graphs are important in healthcare for understanding multimorbidity and comorbidity. To support the visual analysis, we collaborated with medical experts to devise two comparative visualization techniques at different stages of the analysis process. First, a progressive visualization method is proposed for comparing multiple state-of-the-art causal discovery algorithms. The method can handle mixed-type datasets comprising both continuous and categorical variables and assist in the creation of a fine-tuned causal graph of a single outcome. Second, a comparative graph layout technique and specialized visual encodings are devised for the quick comparison of multiple causal graphs. In our visual analysis approach, analysts start by building individual causal graphs for each outcome variable, and then, multi-outcome causal graphs are generated and visualized with our comparative technique for analyzing differences and commonalities of these causal graphs. Evaluation includes quantitative measurements on benchmark datasets, a case study with a medical expert, and expert user studies with real-world health research data.

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 / 2 minor

Summary. The paper introduces a visual analysis method for multi-outcome causal graphs, with emphasis on healthcare applications such as multimorbidity and comorbidity. It presents two expert-collaborated comparative visualization techniques: (1) a progressive visualization method for comparing multiple causal discovery algorithms on mixed-type (continuous/categorical) datasets to produce a fine-tuned single-outcome graph, and (2) a comparative graph layout with specialized encodings to analyze differences and commonalities across graphs for different outcome variables. The workflow builds individual causal graphs per outcome then applies the comparative technique. Evaluation consists of quantitative measurements on benchmark datasets, one medical-expert case study, and expert user studies on real-world health data.

Significance. If the visualizations are shown to be effective, the work could provide a useful applied contribution to visual analytics for causal graphs in medicine by addressing multi-outcome scenarios. Positive elements include the collaboration with domain experts and grounding in real-world health datasets. The significance is limited by the current evaluation's reliance on qualitative feedback rather than controlled performance data.

major comments (2)
  1. [Evaluation] Evaluation section: the paper states that quantitative measurements were performed on benchmark datasets and that expert user studies were conducted, yet supplies no specific performance numbers, error rates, or statistical comparisons to baseline layouts (e.g., side-by-side or matrix views). This leaves the central claim that the two comparative techniques 'effectively support quick comparison of differences and commonalities' without falsifiable support.
  2. [Abstract and Evaluation] Abstract and Evaluation: the assertions that the progressive algorithm comparison and specialized graph layout 'assist in the creation of a fine-tuned causal graph' and enable 'quick comparison' rest on qualitative expert feedback and case studies; no controlled experiments measuring task completion time, accuracy, or insight quality versus alternatives are described, making the effectiveness claim load-bearing but unsupported by the reported evidence.
minor comments (2)
  1. The abstract references 'quantitative measurements' without including any concrete results, tables, or figures; a brief summary of key metrics should be added for readers.
  2. Figure captions and axis labels in the comparative layout figures should explicitly indicate which encodings represent differences versus commonalities to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on the evaluation. We address each point below and will revise the manuscript to strengthen the reported evidence.

read point-by-point responses
  1. Referee: [Evaluation] Evaluation section: the paper states that quantitative measurements were performed on benchmark datasets and that expert user studies were conducted, yet supplies no specific performance numbers, error rates, or statistical comparisons to baseline layouts (e.g., side-by-side or matrix views). This leaves the central claim that the two comparative techniques 'effectively support quick comparison of differences and commonalities' without falsifiable support.

    Authors: We agree that specific numerical results from the benchmark datasets should be reported explicitly rather than only stated as having been performed. The quantitative measurements consist of standard causal discovery metrics (e.g., structural Hamming distance, precision, recall) computed against ground-truth graphs on mixed-type benchmark data. In the revision we will add tables or figures with these concrete values and any direct comparisons to baseline layouts that can be computed from the existing data. revision: yes

  2. Referee: [Abstract and Evaluation] Abstract and Evaluation: the assertions that the progressive algorithm comparison and specialized graph layout 'assist in the creation of a fine-tuned causal graph' and enable 'quick comparison' rest on qualitative expert feedback and case studies; no controlled experiments measuring task completion time, accuracy, or insight quality versus alternatives are described, making the effectiveness claim load-bearing but unsupported by the reported evidence.

    Authors: The current evaluation follows common practice in visual analytics by combining quantitative benchmark metrics with expert case studies and user studies on real health data. We acknowledge that controlled experiments with task time/accuracy measures versus baselines are absent. We will revise the abstract and evaluation section to moderate the wording of effectiveness claims, explicitly describe the evidence types used, and list the lack of controlled experiments as a limitation. revision: yes

Circularity Check

0 steps flagged

No circularity: applied visualization design with independent evaluations

full rationale

The paper introduces a visual analysis method and two comparative visualization techniques for multi-outcome causal graphs, developed through expert collaboration. It reports evaluations via quantitative measurements on benchmark datasets, a medical-expert case study, and expert user studies, without any mathematical derivations, predictions, fitted parameters, or first-principles results that could reduce to inputs by construction. No self-citation chains, uniqueness theorems, or ansatzes are invoked as load-bearing elements. The approach is self-contained as a design contribution in visualization, with no evidence of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The method rests on standard assumptions from causal discovery and information visualization literature plus the premise that expert-informed visual encodings will reveal meaningful graph differences.

axioms (2)
  • domain assumption Causal discovery algorithms produce comparable outputs on mixed continuous-categorical data that can be progressively visualized
    Underpins the first technique described in the abstract
  • domain assumption Specialized graph layouts and encodings can surface commonalities and differences across multiple outcome-specific causal graphs
    Underpins the second technique and overall workflow

pith-pipeline@v0.9.0 · 5727 in / 1211 out tokens · 25858 ms · 2026-05-23T22:40:55.134443+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

80 extracted references · 80 canonical work pages · 1 internal anchor

  1. [1]

    Alexander and M

    E. Alexander and M. Gleicher. Task-driven comparison of topic models. IEEE Transactions on Visualization and Computer Graphics, 22(1):320– 329, 2016. doi: 10.1109/TVCG.2015.2467618 3 7https://www.ukbiobank.ac.uk

  2. [2]

    Alper, B

    B. Alper, B. Bach, N. Henry Riche, T. Isenberg, and J.-D. Fekete. Weighted graph comparison techniques for brain connectivity analysis. In Proceed- ings of the SIGCHI Conference on Human Factors in Computing Systems, CHI ’13, p. 483–492. Association for Computing Machinery, New York, NY , USA, 2013. doi: 10.1145/2470654.2470724 3, 4, 5

  3. [3]

    Andrews, J

    B. Andrews, J. Ramsey, and G. F. Cooper. Scoring Bayesian networks of mixed variables. International Journal of Data Science and Analytics, 6(1):3–18, 2018. doi: 10.1007/s41060-017-0085-7 2

  4. [4]

    Andrews, J

    B. Andrews, J. Ramsey, and G. F. Cooper. Learning high-dimensional directed acyclic graphs with mixed data-types. In Proceedings of Ma- chine Learning Research, vol. 104 of Proceedings of Machine Learning Research, pp. 4–21. PMLR, 2019. 2

  5. [5]

    Andrews, M

    K. Andrews, M. Wohlfahrt, and G. Wurzinger. Visual graph comparison. In 13th International Conference Information Visualisation, pp. 62–67,

  6. [6]

    doi: 10.1109/IV.2009.108 3

  7. [7]

    J. Bae, T. Helldin, and M. Riveiro. Understanding indirect causal rela- tionships in node-link graphs. Computer Graphics Forum, 36(3):411–421,

  8. [8]

    doi: 10.1111/cgf.13198 2, 3

  9. [9]

    Barsky, T

    A. Barsky, T. Munzner, J. Gardy, and R. Kincaid. Cerebral: Visualizing multiple experimental conditions on a graph with biological context. IEEE Transactions on Visualization and Computer Graphics, 14(6):1253–1260,

  10. [10]

    doi: 10.1109/TVCG.2008.117 6

  11. [11]

    Barth, M

    W. Barth, M. Jünger, and P. Mutzel. Simple and efficient bilayer cross counting. In M. T. Goodrich and S. G. Kobourov, eds., Revised Papers from the 10th International Symposium on Graph Drawing, pp. 130–141. Springer-Verlag, Berlin, Heidelberg, 2002. doi: 10.1007/3-540-36151 -0_13 4

  12. [12]

    Bello, B

    K. Bello, B. Aragam, and P. Ravikumar. DAGMA: learning DAGs via M- matrices and a log-determinant acyclicity characterization. In Proceedings of the 36th International Conference on Neural Information Processing Systems, number 598 in NIPS ’22, pp. 8226–8239. Curran Associates Inc., Red Hook, NY , USA, 2024. doi: doi/10.5555/3600270.3600868 2

  13. [13]

    Borland, A

    D. Borland, A. Z. Wang, and D. Gotz. Using counterfactuals to improve causal inferences from visualizations. IEEE Computer Graphics and Applications, 44(1):95–104, 2024. doi: 10.1109/MCG.2023.3338788 2

  14. [14]

    Brandes and B

    U. Brandes and B. Köpf. Fast and simple horizontal coordinate assignment. In P. Mutzel, M. Jünger, and S. Leipert, eds.,Graph Drawing, pp. 31–44. Springer, Berlin, Heidelberg, 2002. doi: 10.1007/3-540-45848-4_3 4, 6

  15. [15]

    Brouillard, S

    P. Brouillard, S. Lachapelle, A. Lacoste, S. Lacoste-Julien, and A. Drouin. Differentiable causal discovery from interventional data. In H. Larochelle, M. Ranzato, R. Hadsell, M. Balcan, and H. Lin, eds., Proceedings of the 34th International Conference on Neural Information Processing Systems, vol. 33, pp. 21865–21877. Curran Associates, Inc., Red Hook, ...

  16. [16]

    doi: doi/abs/10.5555/3495724.3497558 2

  17. [17]

    S. Busetti. Causality is good for practice: policy design and reverse engineering. Policy Sciences, 56(2):419–438, 2023. doi: 10.1007/s11077 -023-09493-7 1

  18. [18]

    Z. Cai, D. Xi, X. Zhu, and R. Li. Causal discoveries for high dimensional mixed data. Statistics in Medicine , 41(24):4924–4940, 2022. doi: 10. 1002/sim.9544 2

  19. [19]

    The Chinese Longitu- dinal Healthy Longevity Survey (CLHLS)-Longitudinal Data (1998-2018) , 2020

    Center for Healthy Aging and Development Studies. The Chinese Longitu- dinal Healthy Longevity Survey (CLHLS)-Longitudinal Data (1998-2018) , 2020. doi: 10.18170/DVN/WBO7LK 1, 7, 11, 15

  20. [20]

    D. M. Chickering. Optimal structure identification with greedy search. Journal of Machine Learning Research, 3:507–554, 2003. 2

  21. [21]

    Y .-L. Chou, C. Moreira, P. Bruza, C. Ouyang, and J. Jorge. Counterfactuals and causability in explainable artificial intelligence: Theory, algorithms, and applications. Information Fusion, 81:59–83, 2022. doi: 10.1016/j. inffus.2021.11.003 1

  22. [22]

    Colombo and M

    D. Colombo and M. H. Maathuis. Order-independent constraint-based causal structure learning. Journal of Machine Learning Research , 15(1):3741–3782, 2014. 4, 10

  23. [23]

    J. A. Cottam, M. Glenski, Z. H. Shaw, R. Rabello, A. Golding, S. V olkova, and D. L. Arendt. Graph comparison for causal discovery. In Proceedings of the Sixth Symposium on Visualization in Data Science, VDS 2021, 2021. 2, 3

  24. [24]

    Z. Deng, D. Weng, X. Xie, J. Bao, Y . Zheng, M. Xu, W. Chen, and Y . Wu. Compass: Towards better causal analysis of urban time series. IEEE Transactions on Visualization and Computer Graphics, 28(1):1051–1061,

  25. [25]

    doi: 10.1109/TVCG.2021.3114875 3

  26. [26]

    IEEE Trans

    E. Gansner, E. Koutsofios, S. North, and K.-P. V o. A technique for drawing directed graphs. IEEE Transactions on Software Engineering, 19(3):214– 230, 1993. doi: 10.1109/32.221135 4

  27. [27]

    E. R. Gansner, Y . Koren, and S. North. Graph drawing by stress majoriza- tion. In J. Pach, ed., Proceedings of the 12th International Conference on Graph Drawing, pp. 239–250. Springer-Verlag, Berlin, Heidelberg, 2004. doi: 10.1007/978-3-540-31843-9_25 6

  28. [28]

    Ghai and K

    B. Ghai and K. Mueller. D-BIAS: A causality-based human-in-the-loop system for tackling algorithmic bias. IEEE Transactions on Visualization and Computer Graphics, 29(1):473–482, 2023. doi: 10.1109/TVCG.2022. 3209484 2

  29. [29]

    Gleicher

    M. Gleicher. Considerations for visualizing comparison. IEEE Transac- tions on Visualization and Computer Graphics, 24(1):413–423, 2018. doi: 10.1109/TVCG.2017.2744199 3

  30. [30]

    Gleicher, D

    M. Gleicher, D. Albers, R. Walker, I. Jusufi, C. D. Hansen, and J. C. Roberts. Visual comparison for information visualization. Information Visualization, 10(4):289–309, 2011. doi: 10.1177/1473871611416549 3, 5

  31. [31]

    G. Guo, E. Karavani, A. Endert, and B. C. Kwon. Causalvis: Visualizations for causal inference. In Proceedings of the 2023 CHI Conference on Human Factors in Computing Systems, number 462 in CHI ’23, pp. 1–20. Association for Computing Machinery, New York, NY , USA, 2023. doi: 10.1145/3544548.3581236 2

  32. [32]

    Hanlon, B

    P. Hanlon, B. I. Nicholl, B. D. Jani, D. Lee, R. McQueenie, and F. S. Mair. Frailty and pre-frailty in middle-aged and older adults and its association with multimorbidity and mortality: a prospective analysis of 493737 UK Biobank participants. The Lancet Public Health, 3(7):e323–e332, 2018. doi: 10.1016/S2468-2667(18)30091-4 3

  33. [33]

    Harrison, M

    C. Harrison, M. Fortin, M. van den Akker, F. Mair, A. Calderon-Larranaga, F. Boland, E. Wallace, B. Jani, and S. Smith. Comorbidity versus multi- morbidity: Why it matters. In Journal of multimorbidity and comorbidity, vol. 11. England, 2021. doi: 10.1177/2633556521993993 2

  34. [34]

    Hascoët and P

    M. Hascoët and P. Dragicevic. Interactive graph matching and visual com- parison of graphs and clustered graphs. InProceedings of the International Working Conference on Advanced Visual Interfaces, A VI ’12, p. 522–529. Association for Computing Machinery, New York, NY , USA, 2012. doi: 10.1145/2254556.2254654 3

  35. [35]

    Holzinger, G

    A. Holzinger, G. Langs, H. Denk, K. Zatloukal, and H. Müller. Causability and explainability of artificial intelligence in medicine. WIREs Data Mining and Knowledge Discovery, 9(4):e1312, 2019. doi: 10.1002/widm. 1312 1

  36. [36]

    M. N. Hoque and K. Mueller. Outcome-Explorer: A causality guided interactive visual interface for interpretable algorithmic decision making. IEEE Transactions on Visualization and Computer Graphics, 28(12):4728– 4740, 2022. doi: 10.1109/TVCG.2021.3102051 2, 3, 9

  37. [37]

    Hyttinen, P

    A. Hyttinen, P. O. Hoyer, F. Eberhardt, and M. Järvisalo. Discovering cyclic causal models with latent variables: a general SAT-based procedure. In Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence, UAI’13, p. 301–310. AUAI Press, Arlington, Virginia, USA,

  38. [38]

    doi: doi/10.5555/3023638.3023669 2

  39. [39]

    Z. Jin, N. Chen, Y . Shi, W. Qian, M. Xu, and N. Cao. TrammelGraph: visual graph abstraction for comparison. Journal of Visualization, 24:365– 379, 2021. doi: 10.1007/s12650-020-00706-2 3

  40. [41]

    Jünger and P

    M. Jünger and P. Mutzel.2-Layer Straightline Crossing Minimization: Per- formance of Exact and Heuristic Algorithms, pp. 3–27. World Scientific,

  41. [42]

    doi: 10.1142/9789812777638_0001 4

  42. [43]

    S. Kaul, D. Borland, N. Cao, and D. Gotz. Improving visualization interpretation using counterfactuals. IEEE Transactions on Visualization and Computer Graphics , 28(1):998–1008, 2022. doi: 10.1109/TVCG. 2021.3114779 2

  43. [44]

    N. R. Ke, O. Bilaniuk, A. Goyal, S. Bauer, H. Larochelle, B. Schölkopf, M. C. Mozer, C. Pal, and Y . Bengio. Learning neural causal models from unknown interventions, 2020. doi: 10.48550/arXiv.1910.01075 2

  44. [45]

    D. Lewis. Causation. The Journal of Philosophy, 70(17):556–567, 1973. doi: 10.2307/2025310 2

  45. [46]

    R. Li, W. Cui, T. Song, X. Xie, R. Ding, Y . Wang, H. Zhang, H. Zhou, and Y . Wu. Causality-based visual analysis of questionnaire responses.IEEE Transactions on Visualization and Computer Graphics, 30(1):638–648,

  46. [47]

    doi: 10.1109/TVCG.2023.3327376 3

  47. [48]

    Y . Li, R. Xia, C. Liu, and L. Sun. A hybrid causal structure learning algorithm for mixed-type data. Proceedings of the 36th AAAI Conference on Artificial Intelligence, 36(7):7435–7443, 2022. doi: 10.1609/aaai.v36i7 .20707 2, 4, 10

  48. [49]

    X. S. Liang and X.-Q. Yang. A note on causation versus correlation in an extreme situation. Entropy, 23(3):316, 2021. doi: 10.3390/e23030316 3

  49. [50]

    Mackinlay

    J. Mackinlay. Automating the design of graphical presentations of rela- tional information. ACM Transactions Graphics, 5(2):110–141, 1986. doi: 10.1145/22949.22950 4

  50. [51]

    T. Munzner. A nested model for visualization design and validation. IEEE Transactions on Visualization and Computer Graphics, 15(6):921–928,

  51. [52]

    doi: 10.1109/TVCG.2009.111 3

  52. [53]

    J. E. Olson, P. Y . Takahashi, and J. M. St Sauver. Understanding the patterns of multimorbidity. In Mayo Clinic Proceedings , vol. 93, pp. 824–825. England, 2018. doi: 10.1016/j.mayocp.2018.05.016 3

  53. [54]

    J. Pearl. Causality. Cambridge University Press, 2nd ed., 2009. doi: 10. 1017/CBO9780511803161 2

  54. [55]

    J. Pearl. An introduction to causal inference. The International Journal of Biostatistics, 6(2), 2010. doi: 10.2202/1557-4679.1203 5

  55. [56]

    Peters, D

    J. Peters, D. Janzing, and B. Schölkopf. Elements of Causal Inference: Foundations and Learning Algorithms. The MIT Press, 2017. 2

  56. [57]

    J. G. Richens, C. M. Lee, and S. Johri. Improving the accuracy of medical diagnosis with causal machine learning. Nature Communications, 11:3923,

  57. [58]

    doi: 10.1038/s41467-020-17419-7 1

  58. [59]

    Richer, A

    G. Richer, A. Pister, M. Abdelaal, J.-D. Fekete, M. Sedlmair, and D. Weiskopf. Scalability in visualization. IEEE Transactions on Vi- sualization and Computer Graphics , 30(7):3314–3330, 2024. doi: 10. 1109/TVCG.2022.3231230 9

  59. [60]

    Sanchez, J

    P. Sanchez, J. P. V oisey, T. Xia, H. I. Watson, A. Q. O’Neil, and S. A. Tsaftaris. Causal machine learning for healthcare and precision medicine. Royal Society Open Science, 9(8):220638, 2022. doi: 10.1098/rsos.220638 1

  60. [61]

    Schober, C

    P. Schober, C. Boer, and L. A. Schwarte. Correlation coefficients: Appro- priate use and interpretation. Anesthesia & Analgesia, 126(5):1763–1768,

  61. [62]

    doi: 10.1213/ANE.0000000000002864 9

  62. [63]

    Sedlmair, M

    M. Sedlmair, M. Meyer, and T. Munzner. Design study methodology: Reflections from the trenches and the stacks. IEEE Transactions on Visualization and Computer Graphics, 18(12):2431–2440, 2012. doi: 10. 1109/TVCG.2012.213 3

  63. [64]

    Shimizu, P

    S. Shimizu, P. O. Hoyer, A. Hyvärinen, and A. Kerminen. A linear non- Gaussian acyclic model for causal discovery.Journal of Machine Learning Research, 7:2003–2030, 2006. doi: doi/10.5555/1248547.1248619 2

  64. [65]

    S. T. Skou, F. S. Mair, M. Fortin, B. Guthrie, B. P. Nunes, J. J. Miranda, C. M. Boyd, S. Pati, S. Mtenga, and S. M. Smith. Multimorbidity. Nature Reviews Disease Primers, 8:48, 2022. doi: 10.1038/s41572-022-00376-4 3

  65. [66]

    Spirtes, C

    P. Spirtes, C. Glymour, and R. Scheines. Causation, Prediction, and Search. Springer-Verlag, New York, 1993. doi: 10.1007/978-1-4612-2748 -9 2, 4, 10

  66. [67]

    Z. Sun, J. Xu, X. Zhang, Z. Dong, and J.-R. Wen. Law article-enhanced legal case matching: A causal learning approach. In Proceedings of the 46th International ACM SIGIR Conference on Research and Development in Information Retrieval, SIGIR ’23, p. 1549–1558. Association for Com- puting Machinery, New York, NY , USA, 2023. doi: 10.1145/3539618. 3591709 1

  67. [68]

    Tazzeo, D

    C. Tazzeo, D. Rizzuto, A. Calderón-Larrañaga, A. Roso-Llorach, A. Marengoni, A.-K. Welmer, G. Onder, C. Trevisan, and D. L. Vetrano. Multimorbidity patterns and risk of frailty in older community-dwelling adults: a population-based cohort study. Age and Ageing, 50(6):2183– 2191, 2021. doi: 10.1093/ageing/afab138 3

  68. [69]

    Tominski, C

    C. Tominski, C. Forsell, and J. Johansson. Interaction support for vi- sual comparison inspired by natural behavior. IEEE Transactions on Visualization and Computer Graphics, 18(12):2719–2728, 2012. doi: 10. 1109/TVCG.2012.237 3

  69. [70]

    Slippage boosted spectral cleaning in a seeded free - electron laser ,

    S. Triantafillou, V . Lagani, C. Heinze-Deml, A. Schmidt, J. Tegner, and I. Tsamardinos. Predicting causal relationships from biological data: Applying automated causal discovery on mass cytometry data of human immune cells. Scientific Reports, 7:12724, 2017. doi: 10.1038/s41598 -017-08582-x 1

  70. [71]

    J. M. Valderas, B. Starfield, B. Sibbald, C. Salisbury, and M. Roland. Defining comorbidity: implications for understanding health and health services. The Annals of Family Medicine, 7(4):357–363, 2009. doi: 10. 1370/afm.983 2, 3

  71. [72]

    D.-B. V o, K. Lazarova, H. C. Purchase, and M. McCann. Visual causality: Investigating graph layouts for understanding causal processes. In A.-V . Pietarinen, P. Chapman, L. Bosveld-de Smet, V . Giardino, J. Corter, and S. Linker, eds., Diagrammatic Representation and Inference, pp. 332–347. Springer International Publishing, Cham, 2020. doi: 10.1007/978-...

  72. [73]

    M. J. V owels, N. C. Camgoz, and R. Bowden. D’ya Like DAGs? A survey on structure learning and causal discovery. ACM Computing Surveys, 55(4):1–36, article no. 82, 2022. doi: 10.1145/3527154 2, 4

  73. [74]

    Wang and K

    J. Wang and K. Mueller. The visual causality analyst: An interactive interface for causal reasoning. IEEE Transactions on Visualization and Computer Graphics, 22(1):230–239, 2016. doi: 10.1109/TVCG.2015. 2467931 2, 3, 9

  74. [75]

    Wang and K

    J. Wang and K. Mueller. Visual causality analysis made practical. In 2017 IEEE Conference on Visual Analytics Science and Technology, V AST, pp. 151–161, 2017. doi: 10.1109/V AST.2017.8585647 2, 3, 9

  75. [76]

    Wang and K

    J. Wang and K. Mueller. DOMINO: Visual causal reasoning with time- dependent phenomena. IEEE Transactions on Visualization and Computer Graphics, 29(12):5342–5356, 2023. doi: 10.1109/TVCG.2022.3207929 2

  76. [77]

    X. Xie, F. Du, and Y . Wu. A visual analytics approach for exploratory causal analysis: Exploration, validation, and applications. IEEE Transac- tions on Visualization and Computer Graphics, 27(2):1448–1458, 2021. doi: 10.1109/TVCG.2020.3028957 2, 3, 9

  77. [78]

    Y . Yu, J. Chen, T. Gao, and M. Yu. DAG-GNN: DAG structure learning with graph neural networks. In K. Chaudhuri and R. Salakhutdinov, eds., Proceedings of the 36th International Conference on Machine Learning, vol. 97 of Proceedings of Machine Learning Research, pp. 7154–7163. PMLR, 2019. doi: 10.48550/arXiv.1904.10098 2, 4, 10

  78. [79]

    Zanga, E

    A. Zanga, E. Ozkirimli, and F. Stella. A survey on causal discovery: Theory and practice. International Journal of Approximate Reasoning, 151:101–129, 2022. doi: 10.1016/j.ijar.2022.09.004 1, 2

  79. [80]

    Zhang, X

    L. Zhang, X. Wang, Y . Liu, G. Zhang, M. Jing, and J. Yu. Vi- sual representation and layout optimization for comparison of dynamic graph. In 2022 IEEE Smartworld, Ubiquitous Intelligence & Com- puting, Scalable Computing & Communications, Digital Twin, Pri- vacy Computing, Metaverse, Autonomous & Trusted Vehicles (Smart- World/UIC/ScalCom/DigitalTwin/Pri...

  80. [81]

    Zheng, B

    X. Zheng, B. Aragam, P. Ravikumar, and E. P. Xing. DAGs with NO TEARS: continuous optimization for structure learning. In Proceedings of the 32nd International Conference on Neural Information Processing Systems, NIPS’18, p. 9492–9503. Curran Associates Inc., Red Hook, NY , USA, 2018. doi: doi/10.5555/3327546.3327618 2, 4, 10 (a) (b) Fig. 8: Visualization...