pith. sign in

arxiv: 2605.03268 · v1 · submitted 2026-05-05 · 💻 cs.LG · cs.AI· stat.ME· stat.ML

Partially Observed Structural Causal Models

Turan Orujlu , Jordan Matelsky , Martin V. Butz , Charley M. Wu , Konrad P. Kording This is my paper

Pith reviewed 2026-05-07 17:28 UTC · model grok-4.3

classification 💻 cs.LG cs.AIstat.MEstat.ML
keywords causal inferencestructural causal modelsidentifiabilitylatent variablesinterventionscausal discoveryneural simulation
0
0 comments X

The pith

Partially Observed Structural Causal Models let researchers identify both causal graphs and mechanisms when latent contexts shape both.

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

The paper defines Partially Observed Structural Causal Models to capture systems where hidden contexts jointly determine the structure of interactions among observed variables and the functional mechanisms that govern them. It extends classical structural causal models with a hierarchy of interventions that can act on nodes, edges, or the latent contexts themselves. A Kolmogorov-Arnold-Sprecher decomposition supplies an explicit parametrization that turns each node mechanism into a sum of univariate functions of its parents, enabling surgical interventions on individual edges. The core theoretical result specifies which families of interventions suffice to separate structure formation from mechanism details. Validation occurs inside a detailed virtual retina simulator that reproduces the expected patterns of identifiability and confounding.

Core claim

We introduce POSCMs as a self-contained causal modeling framework for endogenous graphs in which latent contexts co-determine both interaction structure and downstream mechanisms on observed variables. We adopt a Kolmogorov-Arnold-Sprecher edge-functional decomposition that yields an explicit parametrization of dyadic functional contributions and thereby permits surgical edge interventions. We supply an identifiability theory that clarifies which intervention families suffice to disentangle structure formation from mechanisms, and we confirm the predicted patterns of identifiability and non-identifiability inside a biophysically detailed virtual human retina simulator.

What carries the argument

The Kolmogorov-Arnold-Sprecher edge-functional decomposition, which represents each node mechanism as a sum of univariate functions of its parents and thereby supplies an explicit parametrization for dyadic contributions under edge interventions.

If this is right

  • Context-level interventions suffice to identify both structure and mechanisms even when the contexts themselves remain unobserved.
  • Node interventions alone produce structure-mechanism confounding whenever edge contexts are latent.
  • Targeted node interventions recover synaptic input-output functions in the retina model once the appropriate intervention family is chosen.

Where Pith is reading between the lines

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

  • The same intervention-design principles could guide experiments on real neural circuits if the simulator is replaced by direct measurements.
  • Existing causal-discovery algorithms that assume fixed graphs may need revision when the graph itself is generated by latent processes.
  • The framework suggests a route to causal modeling in domains such as developmental biology where both wiring and function emerge from unobserved contexts.

Load-bearing premise

The claims rest on the assumption that the biophysically detailed virtual retina simulator accurately reproduces the relevant causal relationships and that the decomposition remains practical for real observed data.

What would settle it

If the same intervention protocols applied inside the retina simulator fail to recover the known synaptic input-output relationships when context-level interventions are withheld, or if they recover them when the theory predicts non-identifiability, the positive and negative identifiability results would be falsified.

Figures

Figures reproduced from arXiv: 2605.03268 by Charley M. Wu, Jordan Matelsky, Konrad P. Kording, Martin V. Butz, Turan Orujlu.

Figure 1
Figure 1. Figure 1: Illustration of the expanded DAG for a 3-node view at source ↗
Figure 2
Figure 2. Figure 2: Distributive law toy example. (e.g., x = 2, x′ = 3, y = z = 1 gives 6 vs. 5). This il￾lustrates why edge interventions are a genuinely stronger primitive: they isolate one causal channel without globally changing the source node. In POSCMs, the analogous sepa￾ration underlies the gap between kernel identification (Theo￾rem 5.4) and identifiability of dyadic message primitives or edge-intervention counterfa… view at source ↗
read the original abstract

Here we introduce Partially Observed Structural Causal Models (POSCMs) that formalize causal systems where latent contexts co-determine both the interaction structure and downstream mechanisms on observed variables. POSCMs provide an extension of structural causal models (SCMs), as a self-contained causal modeling framework for endogenous graphs, allowing for an intervention hierarchy spanning node- and edge-level context and endogenous variable interventions. To enable surgical edge interventions, we adopt a Kolmogorov-Arnold-Sprecher edge-functional decomposition, an existence theorem for representing each node mechanism as a sum of univariate functions of its parents, yielding an explicit parametrization of dyadic functional contributions. We provide an identifiability theory that clarifies which intervention families would suffice to disentangle structure formation from mechanisms. We empirically validate these predictions in a biophysically detailed virtual human retina simulator, constructing intervention protocols that (i) reproduce the non-identifiability predicted when context is latent and no context-level interventions are available, (ii) exhibit structure-mechanism confounding under latent edges when only node interventions are observed, and (iii) recover synaptic input-output relationships via targeted node interventions, consistent with our positive kernel identifiability result. Our work generalizes SCMs in a way that allows it to work in a world closer to the one we live in.

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

3 major / 2 minor

Summary. The paper introduces Partially Observed Structural Causal Models (POSCMs) as an extension of standard SCMs in which latent contexts co-determine both the endogenous interaction graph and the mechanisms on observed variables. It adopts the Kolmogorov-Arnold-Sprecher theorem to obtain an explicit univariate decomposition of each node mechanism, thereby parametrizing dyadic edge contributions, and supplies an identifiability theory that characterizes the intervention families (node, edge, and context) sufficient to disentangle structure formation from mechanisms. The theory is tested empirically by constructing intervention protocols inside a biophysically detailed virtual human retina simulator that reproduce the predicted non-identifiability under latent context, the structure-mechanism confounding under node-only interventions, and the recovery of synaptic relationships under targeted interventions.

Significance. If the identifiability results are correct and the empirical checks are faithful to the POSCM assumptions, the framework would constitute a meaningful generalization of SCMs to settings with endogenous, partially observed structure—an important step for causal modeling in neuroscience, biology, and other domains where context modulates connectivity. The explicit KAS parametrization and the intervention hierarchy are concrete contributions that could support future algorithmic work. The paper’s strength lies in its attempt to link theory directly to a detailed simulator; its impact will depend on whether that link is shown to be tight.

major comments (3)
  1. [§4] §4 (Empirical Validation): The retina simulator is reported to implement fixed synaptic connectivity. Standard biophysical retina models do not contain latent-context-dependent endogenous edge formation as required by the POSCM definition in §2. Consequently the three reported intervention outcomes only probe a restricted case and do not confirm that the positive kernel identifiability result holds when structure itself is endogenous and partially observed.
  2. [§3] §3 (Identifiability Theory): The claim that the KAS decomposition yields a practical parametrization for real data is central to the positive identifiability result, yet the manuscript provides no derivation showing how the decomposition reduces to quantities observable under the intervention hierarchy or avoids circular dependence on quantities defined by the authors’ prior work. Without this step the theory remains formal rather than operational.
  3. [§2] §2 (POSCM Definition): The model assumes that latent contexts modulate both the graph and the mechanisms, but the manuscript does not supply an explicit construction or axiom set showing how such context-dependent edge formation is realized inside the simulator used for validation. This gap makes the empirical checks non-diagnostic for the general POSCM case.
minor comments (2)
  1. [§2 and §4] The notation distinguishing node interventions, edge interventions, and context interventions is introduced in §2 but used inconsistently in the empirical section; a single table summarizing the intervention types and their observational consequences would improve clarity.
  2. [§3] No pseudocode or parameter settings for the KAS decomposition are supplied, making it difficult to assess computational feasibility or reproducibility of the edge-functional representation.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment point by point below, indicating the revisions we will incorporate to clarify scope, strengthen derivations, and address gaps in the presentation.

read point-by-point responses

  1. Referee: [§4] §4 (Empirical Validation): The retina simulator is reported to implement fixed synaptic connectivity. Standard biophysical retina models do not contain latent-context-dependent endogenous edge formation as required by the POSCM definition in §2. Consequently the three reported intervention outcomes only probe a restricted case and do not confirm that the positive kernel identifiability result holds when structure itself is endogenous and partially observed.

    Authors: We agree that the retina simulator implements fixed synaptic connectivity and does not feature endogenous edge formation driven by latent contexts. Our reported experiments therefore validate the identifiability predictions only for the fixed-graph case, where latent contexts modulate mechanisms but not structure. This still demonstrates the predicted non-identifiability under latent context, the confounding under node-only interventions, and recovery under targeted interventions. We will revise §4 to explicitly state this scope limitation, add a dedicated paragraph on the implications for fully endogenous POSCMs, and note that simulators with dynamic connectivity would be needed for complete validation of the general case. revision: yes

  2. Referee: [§3] §3 (Identifiability Theory): The claim that the KAS decomposition yields a practical parametrization for real data is central to the positive identifiability result, yet the manuscript provides no derivation showing how the decomposition reduces to quantities observable under the intervention hierarchy or avoids circular dependence on quantities defined by the authors’ prior work. Without this step the theory remains formal rather than operational.

    Authors: The referee correctly notes the absence of an explicit derivation linking the KAS decomposition to observable interventional quantities. We will add a new appendix containing a step-by-step derivation that shows how the univariate functions are recoverable from the intervention hierarchy (node, edge, and context interventions). The derivation will establish identifiability of the dyadic terms directly from the resulting distributions and will not rely on circular references to prior results. This addition will render the parametrization operational and address the concern that the theory remains purely formal. revision: yes

  3. Referee: [§2] §2 (POSCM Definition): The model assumes that latent contexts modulate both the graph and the mechanisms, but the manuscript does not supply an explicit construction or axiom set showing how such context-dependent edge formation is realized inside the simulator used for validation. This gap makes the empirical checks non-diagnostic for the general POSCM case.

    Authors: We acknowledge that the manuscript does not provide an explicit construction or axiom set for context-dependent edge formation, and that the simulator employs fixed connectivity. We will revise §2 to include a formal axiomatic description together with a constructive example (a context-conditioned probabilistic graph model) that realizes latent-context modulation of edges. This will separate the general POSCM definition from the simulator implementation and clarify that the empirical section validates the mechanism-identifiability aspects under fixed structure. revision: yes

Circularity Check

0 steps flagged

No circularity detected in derivation chain

full rationale

The paper introduces POSCMs as a direct extension of standard SCMs to incorporate latent contexts that jointly influence endogenous graph structure and mechanisms. It invokes the Kolmogorov-Arnold-Sprecher theorem solely as an external existence result to obtain an explicit parametrization for edge interventions, without deriving or redefining that theorem from the current work. The identifiability theory is stated as a new contribution that specifies sufficient intervention families, and the empirical section tests its predictions against a simulator without any reduction of those predictions to parameters fitted from the same data or to self-citations whose content is presupposed. No self-definitional loops, fitted-input-as-prediction patterns, or load-bearing self-citation chains appear in the abstract or described framework; the derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the Kolmogorov-Arnold-Sprecher representation theorem as a standard mathematical tool and on the introduction of the POSCM class itself; no explicit free parameters are described in the abstract.

axioms (1)
  • standard math Kolmogorov-Arnold-Sprecher theorem guarantees that any multivariate function can be expressed as a sum of univariate functions of its arguments
    Invoked to obtain an explicit parametrization of dyadic functional contributions for edge interventions
invented entities (1)
  • Partially Observed Structural Causal Models (POSCMs) no independent evidence
    purpose: Formalize causal systems in which latent contexts co-determine both interaction structure and downstream mechanisms
    New modeling class introduced by the paper

pith-pipeline@v0.9.0 · 5546 in / 1392 out tokens · 66603 ms · 2026-05-07T17:28:05.177643+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

125 extracted references · 30 canonical work pages

  1. [1]

    Causal Discovery with Linear Non-

    Zhang, Kun and Hyv. Causal Discovery with Linear Non-. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence , pages=

  2. [2]

    Advances in Neural Information Processing Systems , volume=

    Differentiable Causal Discovery from Interventional Data , author=. Advances in Neural Information Processing Systems , volume=

  3. [3]

    Journal of Machine Learning Research , volume=

    Learning the Structure of Linear Latent Variable Models , author=. Journal of Machine Learning Research , volume=

  4. [4]

    2000 , publisher=

    Causation, Prediction, and Search , author=. 2000 , publisher=

    2000

  5. [5]

    Journal of Machine Learning Research , volume=

    Optimal Structure Identification with Greedy Search , author=. Journal of Machine Learning Research , volume=

  6. [6]

    Journal of Machine Learning Research , volume=

    Active Learning of Causal Networks with Intervention Experiments and Optimal Designs , author=. Journal of Machine Learning Research , volume=

  7. [7]

    Advances in Neural Information Processing Systems , volume=

    Sample Efficient Active Learning of Causal Trees , author=. Advances in Neural Information Processing Systems , volume=

  8. [8]

    Active Learning for Structure in

    Tong, Simon and Koller, Daphne , booktitle=. Active Learning for Structure in

  9. [9]

    Artificial Intelligence , volume=

    Planning and Acting in Partially Observable Stochastic Domains , author=. Artificial Intelligence , volume=

  10. [10]

    Hidden Parameter

    Doshi-Velez, Finale and Konidaris, George , booktitle=. Hidden Parameter

  11. [11]

    Moss, Henry B and Leslie, David S and Rayson, Paul , journal=

  12. [12]

    2009 , publisher=

    Causality: Models, Reasoning and Inference , author=. 2009 , publisher=

    2009

  13. [13]

    2008 , publisher=

    Introduction to Nonparametric Estimation , author=. 2008 , publisher=

    2008

  14. [14]

    2007 , school=

    Causation and Intervention , author=. 2007 , school=

    2007

  15. [15]

    Perturb-seq: Dissecting Molecular Circuits with Scalable Single-Cell

    Dixit, Atray and Parnas, Oren and Li, Biyu and Chen, Jenny and Fulco, Charles P and Jerby-Arnon, Livnat and Marjanovic, Nemanja D and Dionne, Danielle and Burks, Tyler and Raychowdhury, Raktima and others , journal=. Perturb-seq: Dissecting Molecular Circuits with Scalable Single-Cell. 2016 , publisher=

    2016

  16. [16]

    Proceedings of the IEEE , volume=

    Toward Causal Representation Learning , author=. Proceedings of the IEEE , volume=

  17. [17]

    International Conference on Learning Representations , year=

    A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms , author=. International Conference on Learning Representations , year=

  18. [18]

    Zheng, Xun and Aragam, Bryon and Ravikumar, Pradeep and Xing, Eric P , booktitle=

  19. [19]

    Characterization and Greedy Learning of Interventional

    Hauser, Alain and B. Characterization and Greedy Learning of Interventional. Journal of Machine Learning Research , volume=

  20. [20]

    1997 , school=

    Graphical Models: Selecting Causal and Statistical Models , author=. 1997 , school=

    1997

  21. [21]

    A Linear Non-

    Shimizu, Shohei and Hoyer, Patrik O and Hyv. A Linear Non-. Journal of Machine Learning Research , volume=

  22. [22]

    Yu, Yue and Chen, Jie and Gao, Tian and Yu, Mo , booktitle=

  23. [23]

    D'ya Like

    Vowels, Matthew J and Camgoz, Necati Cihan and Bowden, Richard , journal=. D'ya Like

  24. [24]

    arXiv preprint arXiv:1910.01075 , year=

    Learning Neural Causal Models from Unknown Interventions , author=. arXiv preprint arXiv:1910.01075 , year=

    work page arXiv 1910

  25. [25]

    Lawrence, Neil D and others , booktitle=

  26. [26]

    Nature Communications , volume=

    Inferring Causation from Time Series in Earth System Sciences , author=. Nature Communications , volume=

  27. [27]

    Theory of Probability & Its Applications , volume=

    Prescribing a System of Random Variables by Conditional Distributions , author=. Theory of Probability & Its Applications , volume=

  28. [28]

    1946 , publisher=

    Mathematical Methods of Statistics , author=. 1946 , publisher=

    1946

  29. [29]

    Bulletin of the Calcutta Mathematical Society , volume=

    Information and the Accuracy Attainable in the Estimation of Statistical Parameters , author=. Bulletin of the Calcutta Mathematical Society , volume=

  30. [30]

    Journal of the American Statistical Association , volume=

    Probability Inequalities for Sums of Bounded Random Variables , author=. Journal of the American Statistical Association , volume=

  31. [31]

    Rademacher, Hans , journal=. Einige

  32. [32]

    1961 , publisher=

    Transmission of Information: A Statistical Theory of Communications , author=. 1961 , publisher=

    1961

  33. [33]

    1998 , publisher=

    Asymptotic Statistics , author=. 1998 , publisher=

    1998

  34. [34]

    1964 , publisher=

    Information and Information Stability of Random Variables and Processes , author=. 1964 , publisher=

    1964

  35. [35]

    2006 , publisher=

    Elements of Information Theory , author=. 2006 , publisher=

    2006

  36. [36]

    2004 , publisher=

    Convex Optimization , author=. 2004 , publisher=

    2004

  37. [37]

    Russian Mathematical Surveys , volume=

    The Method of Reflection Positivity in the Mathematical Theory of First-Order Phase Transitions , author=. Russian Mathematical Surveys , volume=

  38. [38]

    Active Learning of Causal

    Murphy, Kevin , institution=. Active Learning of Causal

  39. [39]

    Journal of Basic Engineering , volume=

    A New Approach to Linear Filtering and Prediction Problems , author=. Journal of Basic Engineering , volume=

  40. [40]

    Sequential

    Doucet, Arnaud and de Freitas, Nando and Gordon, Neil , year=. Sequential

  41. [41]

    2004 , publisher=

    Monte Carlo Statistical Methods , author=. 2004 , publisher=

    2004

  42. [42]

    arXiv preprint arXiv:0709.3380 , year=

    The causal manipulation of chain event graphs , author=. arXiv preprint arXiv:0709.3380 , year=

    work page arXiv

  43. [43]

    Revisiting Classifier Two-Sample Tests , booktitle =

    David Lopez. Revisiting Classifier Two-Sample Tests , booktitle =. 2017 , url =

    2017

  44. [44]

    Borgwardt and Malte J

    Arthur Gretton and Karsten M. Borgwardt and Malte J. Rasch and Bernhard Sch. A Kernel Two-Sample Test , journal =. 2012 , url =. doi:10.5555/2503308.2188410 , timestamp =

    work page doi:10.5555/2503308.2188410 2012

  45. [45]

    Ho, Peter and Raftery, Adrian and H, Mark , year =

  46. [46]

    Young and Edward R

    Stephen J. Young and Edward R. Scheinerman , editor =. Random Dot Product Graph Models for Social Networks , booktitle =. 2007 , url =. doi:10.1007/978-3-540-77004-6\_11 , timestamp =

    work page doi:10.1007/978-3-540-77004-6 2007

  47. [47]

    The Origins of Order: Self-Organization and Selection in Evolution , volume =

    Kauffman, Stuart , year =. The Origins of Order: Self-Organization and Selection in Evolution , volume =. emergence.org , doi =

  48. [48]

    Random Networks of Automata: A Simple Annealed Approximation , volume =

    Derrida, Bernard and Pomeau, Yves , year =. Random Networks of Automata: A Simple Annealed Approximation , volume =. EPL (Europhysics Letters) , doi =

  49. [49]

    The Theory of Branching Process

    Harris, Theodore Edward. The Theory of Branching Process. 1964

    1964

  50. [50]

    Monte Carlo methods in financial engineering , url =

    Glasserman, Paul , biburl =. Monte Carlo methods in financial engineering , url =

  51. [51]

    Markov Graphs , volume =

    Frank, Ove and Strauss, David , year =. Markov Graphs , volume =. JASA. Journal of the American Statistical Association , doi =

  52. [52]

    Large Networks and Graph Limits , series =

    L. Large Networks and Graph Limits , series =. 2012 , url =

    2012

  53. [53]

    Graph limits and exchangeable random graphs , volume =

    Diaconis, Persi and Janson, Svante , year =. Graph limits and exchangeable random graphs , volume =

  54. [54]

    MATRIX ESTIMATION BY UNIVERSAL SINGULAR VALUE THRESHOLDING , urldate =

    Sourav Chatterjee , journal =. MATRIX ESTIMATION BY UNIVERSAL SINGULAR VALUE THRESHOLDING , urldate =

  55. [55]

    2025 , eprint=

    Wavelet Latent Position Exponential Random Graphs , author=. 2025 , eprint=

    2025

  56. [56]

    2024 , eprint=

    Noise-free comparison of stochastic agent-based simulations using common random numbers , author=. 2024 , eprint=

    2024

  57. [57]

    Fellows , title =

    Ian E. Fellows , title =. CoRR , volume =. 2018 , url =. 1804.04583 , timestamp =

    work page arXiv 2018

  58. [58]

    Transfer Learning on Edge Connecting Probability Estimation under Graphon Model , journal =

    Yuyao Wang and Yu. Transfer Learning on Edge Connecting Probability Estimation under Graphon Model , journal =. 2025 , url =. doi:10.48550/ARXIV.2510.05527 , eprinttype =. 2510.05527 , timestamp =

    work page doi:10.48550/arxiv.2510.05527 2025

  59. [59]

    2025 , eprint=

    Logistic-beta processes for dependent random probabilities with beta marginals , author=. 2025 , eprint=

    2025

  60. [60]

    2025 , eprint=

    The effects of initial conditions on the accuracy of mean-field approximations of Markov processes on large random graphs , author=. 2025 , eprint=

    2025

  61. [61]

    Vincent Poor , title =

    H. Vincent Poor , title =. Autom. , volume =. 1996 , url =. doi:10.1016/0005-1098(96)82332-6 , timestamp =

    work page doi:10.1016/0005-1098(96)82332-6 1996

  62. [62]

    2007 , eprint=

    Bayesian Online Changepoint Detection , author=. 2007 , eprint=

    2007

  63. [63]

    Journal of the Royal Statistical Society Series B: Statistical Methodology , volume =

    Peters, Jonas and Bühlmann, Peter and Meinshausen, Nicolai , title =. Journal of the Royal Statistical Society Series B: Statistical Methodology , volume =. 2016 , month =. doi:10.1111/rssb.12167 , url =

    work page doi:10.1111/rssb.12167 2016

  64. [64]

    Hudgens and M

    Michael G. Hudgens and M. Elizabeth Halloran , journal =. Toward Causal Inference with Interference , urldate =

  65. [65]

    Characterization and greedy learning of interventional Markov equivalence classes of directed acyclic graphs , journal =

    Alain Hauser and Peter B. Characterization and greedy learning of interventional Markov equivalence classes of directed acyclic graphs , journal =. 2012 , url =. doi:10.5555/2503308.2503320 , timestamp =

    work page doi:10.5555/2503308.2503320 2012

  66. [66]

    CoRR , volume =

    Peter B. CoRR , volume =. 2013 , url =. 1310.1533 , timestamp =

    work page arXiv 2013

  67. [67]

    Rastko Ciric, Daniel H

    Carroll, Raymond J. and Ruppert, David and Stefanski, Leonard A. and Crainiceanu, Ciprian M. , biburl =. Measurement Error in Nonlinear Models , url =. doi:10.1201/9781420010138 , interhash =

    work page doi:10.1201/9781420010138

  68. [68]

    David Maxwell Chickering , title =. J. Mach. Learn. Res. , volume =. 2002 , url =

    2002

  69. [69]

    Correa and Elias Bareinboim , editor =

    Juan D. Correa and Elias Bareinboim , editor =. General Transportability of Soft Interventions: Completeness Results , booktitle =. 2020 , url =

    2020

  70. [70]

    Decision-theoretic foundations for statistical causality , volume =

    Dawid, Alexander , year =. Decision-theoretic foundations for statistical causality , volume =. Journal of Causal Inference , doi =

  71. [71]

    Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics,

    Elias Bareinboim and Judea Pearl , title =. Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics,. 2013 , url =

    2013

  72. [72]

    A General Identification Algorithm For Data Fusion Problems Under Systematic Selection , booktitle =

    Jaron Jia Rong Lee and AmirEmad Ghassami and Ilya Shpitser , editor =. A General Identification Algorithm For Data Fusion Problems Under Systematic Selection , booktitle =. 2024 , url =

    2024

  73. [73]

    Higher-order causal structure learning with additive models

    James Enouen and Yujia Zheng and Ignavier Ng and Yan Liu and Kun Zhang , title =. CoRR , volume =. 2025 , url =. doi:10.48550/ARXIV.2511.03831 , eprinttype =. 2511.03831 , timestamp =

    work page doi:10.48550/arxiv.2511.03831 2025

  74. [74]

    Characterization and Learning of Causal Graphs with Latent Variables from Soft Interventions , booktitle =

    Murat Kocaoglu and Amin Jaber and Karthikeyan Shanmugam and Elias Bareinboim , editor =. Characterization and Learning of Causal Graphs with Latent Variables from Soft Interventions , booktitle =. 2019 , url =

    2019

  75. [75]

    Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence , pages =

    Maier, Marc and Marazopoulou, Katerina and Arbour, David and Jensen, David , title =. Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence , pages =. 2013 , publisher =

    2013

  76. [76]

    Mooij and Sara Magliacane and Tom Claassen , title =

    Joris M. Mooij and Sara Magliacane and Tom Claassen , title =. J. Mach. Learn. Res. , volume =. 2020 , url =

    2020

  77. [77]

    External Validity: From

    Judea Pearl and Elias Bareinboim , editor =. External Validity: From. Probabilistic and Causal Inference: The Works of Judea Pearl , series =. 2022 , url =. doi:10.1145/3501714.3501741 , timestamp =

    work page doi:10.1145/3501714.3501741 2022

  78. [78]

    Chain event graphs

    Collazo, Rodrigo A and Goergen, Christiane and Smith, Jim Q. Chain event graphs

  79. [79]

    Schennach , journal =

    Susanne M. Schennach , journal =. Recent Advances in the Measurement Error Literature , urldate =

  80. [80]

    Toward Causal Representation Learning , journal =

    Bernhard Sch. Toward Causal Representation Learning , journal =. 2021 , url =. doi:10.1109/JPROC.2021.3058954 , timestamp =

    work page doi:10.1109/jproc.2021.3058954 2021

Showing first 80 references.