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What is causal about causal models and representations?

T0 review · 2 major / 3 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read This paper proves that the natural mapping from interventions to real-world actions is circular: every compatible causal Bayesian network is trivially interventionally valid, so interventional data cannot falsify it, and any non-circular…

desk verdict The framework and the circularity of IntC are solid, but the headline impossibility result (Prop 4.1) is false as stated: D1–D4 can be satisfied vacuously by a non-circular interpretation. read the letter →

arxiv 2501.19335 v2 pith:UTAQTC6O submitted 2025-01-31 stat.ML cs.AIcs.LGmath.STstat.TH

Frederik Hytting J{o}rgensen , Luigi Gresele , Sebastian Weichwald This is my paper · ORCID
classification stat.MLcs.AIcs.LGmath.STstat.TH MSC 62A0162D20
keywords causalBayesiannetworksinterventionsinterventionalvalidityfalsifiabilityrepresentationlearningabstractioncircularityinterpretationofactions
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Causal Bayesian networks are called causal because they predict what happens under interventions. This paper asks what it means for an action in the world to count as an intervention in the model, and it shows that the most intuitive answer is self-defeating. Under the interpretation IntC, an action counts as an intervention exactly when it produces the distribution the model assigns to that intervention; the authors prove that then every network that matches the observational distribution also matches every interventional distribution by construction, so no experiment can ever falsify it. They further prove an impossibility theorem: any interpretation that satisfies four natural desiderata—if it behaves like an intervention it is one, an action is not mapped to distinct interventions with different distributions, the mapping does not depend on the intervention set, and interventions do not create new dependencies—must coincide with IntC and hence be circular. The paper then studies non-circular interpretations that relax one desideratum, showing how falsification becomes possible, and draws consequences for causal discovery, causal representation learning, and causal abstraction.

What carries the argument

The central object is the interpretation Int, a mapping that assigns to each action a subset of the modeled interventions of a CBN, together with the definition of interventional validity: a model $C$ is $I-\mathrm{Int}$ valid for representation $Z^*$ if every action interpreted as intervention $d\in I$ indeed induces the interventional distribution $L_{C;d}(Z)$. The proof engine is Proposition 3.2, which identifies the natural interpretation $\mathrm{IntC}$ with the condition $L_a(Z^*)=L_{C;d}(Z)$, and Proposition 4.1, which shows that the four desiderata D1–D4 force an interpretation to coincide with $\mathrm{IntC}$. The desiderata formalize 'if it behaves like an intervention, it is that intervention' (D1), 'an action is not interpreted as distinct interventions with different distributions' (D2), 'interpretations do not depend on the ambient intervention set' (D3), and 'interventions do not create new dependencies' (D4). Together they pin down the circular interpretation, and the paper's non-circular alternatives each drop exactly one of D1–D4 (or introduce a complexity measure on actions, as in IntK).

What would settle it

Enumerate all two-node binary causal Bayesian networks with finite intervention sets and finite action sets, and search for an interpretation satisfying desiderata D1–D4 whose assignment differs from $\mathrm{IntC}$ on some action; Proposition 4.1 guarantees this search fails, so the first counterexample found would refute the impossibility result and, with it, the paper's central conclusion.

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Extended reading notes

Core claim

The paper's central claim is that interventional validity—the property that a causal Bayesian network correctly predicts the distribution of a representation under an action—is not an intrinsic property of the model but a joint property of the model, the data-generating process, and an interpretation that maps actions to interventions. The seemingly natural interpretation IntC, which reads an action as intervention $d$ exactly when the action induces the same distribution over the representation as the model under $d$, is circular: by Proposition 3.2, $d\in\mathrm{IntI}_C(a)$ iff $L_a(Z^*)=L_{C;d}(Z)$, and therefore every CBN compatible with the observational distribution is $I-\mathrm{IntC}$ valid for every set of interventions $I$. Consequently, interventional data cannot falsify such models. The impossibility result (Proposition 4.1) strengthens this: any interpretation satisfying desiderata D1–D4 must coincide with IntC, so no reasonable-looking interpretation can escape circularity without dropping at least one desideratum. Non-circular alternatives that violate D1 (perfect interventions, IntP), D2 (single-node interventions, IntS), D3 (order-based Int eI,f), or D4 (Markov, IntM) are shown to allow falsification in specific settings, and a complexity-based interpretation IntK connects to minimal-change semantics of conditionals.

Load-bearing premise

The framework treats a data-generating process as nothing more than a set of actions together with the distributions they induce on low-level features; if real actions carry additional structure beyond the distributions they produce—such as the mechanism by which they are implemented, temporal ordering, or the experimenter's intentions—that structure is invisible to the framework and could in principle break the circularity, so the impossibility claim depends entirely on this distribution-only characterization.

Editorial extensions

If this is right

  • If Proposition 4.1 is correct, the common assumption that interventional predictions allow falsification of causal models only holds after one has explicitly chosen a non-circular interpretation such as IntP, IntS, or IntK; absent that choice, interventional validity is vacuous because every compatible model is trivially valid.
  • Identifiability of a causal representation up to transformations like the ∼CRL equivalence class does not guarantee interventional validity: representations that are indistinguishable for identification purposes can differ in whether they admit a causally valid model, so identifiability analyses should be complemented by validity checks over the full action set.
  • Causal abstraction maps between low-level and high-level models can turn an interventionally valid model into an invalid one, and existing notions such as τ-abstraction rest on an infinite regress of interpretations; framing abstraction as preservation or induction of interventional validity suggests new constraints for model transformations.
  • A representation being 'causal' is not a property of the representation alone but of the pair of a representation and an interpretation; the paper's Definition 6.3 is the first formal definition of causal representation based on interventional validity rather than stipulating a ground-truth latent variable.

Reading between the lines

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

  • Read as a no-free-lunch result, the impossibility theorem suggests that the difficulty of grounding interventions is a structural feature of interventional distributions, not a technical gap: causal discovery should therefore be reframed as jointly choosing an interpretation and a graph rather than treating graphs as primary.
  • The complexity-based interpretation IntK invites a concrete bridge to algorithmic information theory: define the complexity K(a) as the description length of the action and test whether models validated under IntK coincide with those selected by algorithmic-independence causal discovery, which would unify the paper's semantics with independence-based methods.
  • For causal representation learning practice, the paper implies the learning target should be a pair (h, Int) that is interventionally valid on held-out actions, not merely identifiable on observed environments; an immediate testable extension is to evaluate existing CRL methods on unseen action sets to check whether their claimed latent graphs remain valid under IntS or IntP.
  • The circularity result also sharpens the interpretation of neuron-level interventions in mechanistic interpretability: those interventions are unambiguous only because the network's own kernels are taken as reference, which is an instance of the circular interpretation, and external justification is needed to privilege that model over alternatives.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 3 minor

Summary. The paper proposes a formal framework for linking actions in a data-generating process to interventions in a causal Bayesian network (CBN), via 'interpretations' that map actions to subsets of model interventions. It defines emulation and interventional validity, and shows that the seemingly natural interpretation IntC (Definition 3.1) is circular: for any compatible CBN, every action that satisfies IntC is automatically predicted correctly, so no empirical data can falsify the model under this interpretation (Corollary 3.3). The paper then introduces five desiderata D0–D4 and claims an impossibility result (Proposition 4.1) that any interpretation satisfying D1–D4 must equal IntC, hence be circular. It subsequently studies non-circular interpretations that violate D1 or D2 (and others in appendices), and discusses implications for causal representation learning, causal discovery, and causal abstraction.

Significance. If the results hold, the paper makes a valuable conceptual contribution by making explicit the often-implicit correspondence between actions and interventions, and by distinguishing emulation (always possible) from interventional validity (substantive). The proof that IntC is circular (Proposition 3.2 and Corollary 3.3) is correct and, to my knowledge, new in its crispness. The framework also yields useful definitions, such as causal representation based on interventional validity (Definition 6.3), and the discussion of non-circular interpretations is insightful. However, the advertised impossibility result is not established: Proposition 4.1 is false as stated, as shown by a simple counterexample below. The paper is not machine-checked, but the proofs are mostly clear and detailed; the main deductive claims that are correct are Propositions 3.2, 5.2, 5.5, and 5.8. Because the impossibility theorem is a central advertised contribution, the manuscript requires substantial revision.

major comments (2)
  1. [Section 4, Proposition 4.1] The proof of Proposition 4.1 contains a false assertion: 'Since La(Z*) is Markov w.r.t. the DAG of C, we can find an intervention b such that LC;b(Z) = La(Z*)'. This fails when La(Z*) equals the observational distribution LC(Z), because Definition 2.1 explicitly requires every intervention to change the distribution, so no intervention b can satisfy LC;b = LC. This is not a mere technicality. Concretely, let C be a single-node CBN with LC(X)=Ber(0.5), let D have actions A={O,a} with LO=La=Ber(0.5), and define Int^I(a) = {do(X←δ0)} if that intervention belongs to I and Int^I(a)=∅ otherwise, with Int^I(O)=∅. Then D1 holds vacuously (no intervention reproduces Ber(0.5)), D2 holds since Int^I(a) has at most one element, D3 holds by construction, and D4 holds vacuously on a single node. Yet for I={do(X←δ0)}, Int^I(a) differs from IntC^I(a)=∅, and C is not I-Int valid for this interpretation because La≠LC;do(X←δ0). Thus D1–D4 do not imply IntC, and the impossibility result as stated is false. The theorem could be repaired by adding D0 as an explicit premise, or by assuming that every action distribution is in the image of the intervention map, but the current claim is unsupported.
  2. [Section 4, sentence following Proposition 4.1] The sentence 'IntC satisfies D0, so desiderata D1–D4 together imply D0' is false for the same reason as the counterexample above: D1–D4 can be satisfied without D0. The derivation of D0 from D1–D4 depends on the invalid existence step in the proof of Proposition 4.1. This conclusion is used to frame the desiderata as redundant, but it is not established.
minor comments (3)
  1. [Proposition 3.2, proof] The proof contains a typographical slip: 'If La(Z*) = LC;d(X)' should read '... = LC;d(Z)'.
  2. [Definition 2.5 and surrounding text] The surjectivity of the link g is required for emulation, but the definition would be clearer if the empty-intervention case (when A \ {O} is empty) were explicitly handled; currently the existence statement below the definition implicitly assumes a nonempty action set.
  3. [Section 5.3, Proposition 5.8] The regularity condition 'La(Z*) has the same finite support for every a' is strong and is not discussed in the main text; a brief remark on why it is needed would help the reader gauge the scope of the result.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper's main results are transparent axiomatic unpackings of its own definitions, not hidden reductions to inputs.

full rationale

The paper's central claim is that the 'seemingly natural' interpretation IntC is circular, and it is explicit about this: Definition 3.1 defines d in IntI_C(a) exactly by the conditions that together are equivalent to La(Z*) = LC;d(Z), and Proposition 3.2 proves that equivalence. Corollary 3.3 then simply unpacks this definition to show every compatible CBN is interventionally valid under IntC. This is the paper's object of study, not a hidden circular step in its own derivation. Proposition 4.1 is an axiomatic implication: D1 states the converse direction of IntC ('if it behaves like an intervention, it is that intervention'), and D2-D4 are used to force the forward direction; the proof is a direct logical argument from stated desiderata, not a reduction of the conclusion to the premises. No parameter is fitted and then renamed a prediction; no empirical claim is derived from fitted values. The self-citations, notably to von Kuegelgen et al. (2024) for the ~CRL equivalence class, are used as background for the causal-representation-learning discussion and are not load-bearing for the main impossibility or circularity theorems. The framework's distributional characterization of actions (Definition 2.3) is an explicitly stated modeling assumption, and the paper's results are conditional on it; acknowledging that real actions may carry extra structure is a limitation, not circular reasoning. A reviewer's objection that Proposition 4.1's proof step 'we can find an intervention b' can fail for actions whose distribution equals the observational distribution is a mathematical correctness concern about edge cases, not a circularity in the paper's derivation. The derivation chain is self-contained and deductive from definitions, so the appropriate finding is no significant circularity.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central theorems rest on the explicit assumption that a data-generating process is fully described by the set of distributions induced by actions (Definition 2.3). No physical entities are postulated and no parameters are fitted to data; the only free input is the complexity measure K used by interpretation IntK in Section 5.3.

free parameters (1)
  • Complexity measure K
    In Definition 5.7, the interpretation IntK depends on an externally supplied complexity measure K: A -> R+ (a positive real number per action). The paper does not specify how to choose K; different choices change interventional validity (Example 5.9). It is a free modeling choice, not fitted to data.
assumptions (5)
  • domain assumption The data-generating process is fully described by the distributions La(X*) for actions a in A.
    Definition 2.3 defines a data-generating process solely as a set of actions and distributions, without any further structure such as mechanisms or temporal ordering.
  • domain assumption Interventions in a CBN are modeled as replacement of kernels, do not change the DAG, and induce distributions different from the observational distribution.
    Definition 2.1 and the paragraph after it; this is a standard but nontrivial modeling choice.
  • domain assumption For every action a, the distribution La(Z*) has a density with respect to a product of sigma-finite measures.
    Assumed in Section 2 before Definition 2.5, needed for the conditional kernel notation.
  • domain assumption The representation Z* = h(X*) is a measurable function of the low-level features.
    Definition 2.4.
  • standard math Standard measure-theoretic probability and graphical model background.
    Used throughout; e.g., Markov kernels, densities, acyclicity.

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Pith. "Pith review of What is causal about causal models and representations?." pith.science (2026). https://pith.science/paper/UTAQTC6O

@misc{pith2026250119335,
  author       = {Pith},
  title        = {Pith review of: What is causal about causal models and representations?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UTAQTC6O}},
  note         = {Machine review of arXiv:2501.19335}
}
read the original abstract

Causal Bayesian networks are 'causal' models since they make predictions about interventional distributions. To connect such causal model predictions to real-world outcomes, we must determine which actions in the world correspond to which interventions in the model. For example, to interpret an action as an intervention on a treatment variable, the action will presumably have to a) change the distribution of treatment in a way that corresponds to the intervention, and b) not change other aspects, such as how the outcome depends on the treatment; while the marginal distributions of some variables may change as an effect. We introduce a formal framework to make such requirements for different interpretations of actions as interventions precise. We prove that the seemingly natural interpretation of actions as interventions is circular: Under this interpretation, every causal Bayesian network that correctly models the observational distribution is trivially also interventionally valid, and no action yields empirical data that could possibly falsify such a model. We prove an impossibility result: No interpretation exists that is non-circular and simultaneously satisfies a set of natural desiderata. Instead, we examine non-circular interpretations that may violate some desiderata and show how this may in turn enable the falsification of causal models. By rigorously examining how a causal Bayesian network could be a 'causal' model of the world instead of merely a mathematical object, our formal framework contributes to the conceptual foundations of causal representation learning, causal discovery, and causal abstraction, while also highlighting some limitations of existing approaches.

Figures

Figures reproduced from arXiv: 2501.19335 by the authors.

Figure 1
Figure 1. The framework presented in this article has three main components. 1) The [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. In Example 5.3, we assume that the low-level representation (LDL∗ , HDL∗ , HD∗ ) is emulated by a CBN A, with graph given in Figure 2a, and single-node interventions in A. Under IntP , we falsify the (TC∗ , HD∗ ) := (LDL∗ + HDL∗ , HD∗ )-compatible CBN C with graph given in Figure 2b. If there exists an action that induces a distribution like an intervention in Proposi￾tion 5.2 (2), that is, a perfect intervention on… view at source ↗
Figure 3
Figure 3. Depiction of the situation in Example 5.9. There are 6 different locations, three on each the left and right side S ∗ , with associated rewards R∗ (+1 or −1). Observationally, the stick figure picks a position P ∗ using a uniform distribution over the 6 locations. Whether the causal model S → R makes correct predictions about interventions on left/right, depends on which specific actions are interpreted as intervent… view at source ↗

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Works this paper leans on

22 extracted references · 19 canonical work pages · cited by 1 Pith paper

  1. [1]

    d ∈ eI ∩IntI S(a), see Definition 5.4

    work page

  2. [2]

    ◦ IntI C(a) ⊆ IntI eI,f (a) such that D1 (if it behaves like an intervention, it is that intervention) is satisfied

    For every b ∈ I \ {d}, if b ∈ eI ∩IntI S(a), then f (b) > f(d). ◦ IntI C(a) ⊆ IntI eI,f (a) such that D1 (if it behaves like an intervention, it is that intervention) is satisfied. To ensure that IntI eI,f (a) is not generally a subset of IntI C(a), we also let d ∈ Ibe in IntI eI,f (a) if two conditions are satisfied. Informally, this works as follows: Fo...

    work page

  3. [3]

    τ : [4] → {0, 1}2 given by x 7→ (1 (x = 3) + 1 (x = 4), 1 (x = 2) + 1 (x = 4)) is clearly surjective

    The third condition of Definition 3.13 in Beckers and Halpern [2019] holds since ωτ is defined for all interventions in I ∗ and we choose IY = ωτ (I ∗). τ : [4] → {0, 1}2 given by x 7→ (1 (x = 3) + 1 (x = 4), 1 (x = 2) + 1 (x = 4)) is clearly surjective. For each d ∈ I∗, we compute ωτ (d) using Definition 3.12 of Beckers and Halpern [2019]: • ωτ (do(X1 = ...

    work page 2019

  4. [5]

    L(Z ∗ 1 ) without altering the joint distribution of ( Z ∗ 1 , Z∗ 2 ) [Lauritzen, 2019]

    This, however, does not follow from the observational distribution LO(Z ∗ 1 , Z∗ 2 ) since conditional distributions of Z ∗ 2 given Z ∗ 1 can always be changed on null sets w.r.t. L(Z ∗ 1 ) without altering the joint distribution of ( Z ∗ 1 , Z∗ 2 ) [Lauritzen, 2019]. In particular, there exists a CBN C such that LO(Z ∗ 1 , Z∗ 2 ) = LC (Z1, Z2) and La(Z ∗...

    work page 2019

  5. [6]

    Green and grue causal variables

    (Cited on page 27.) Frederick Eberhardt. Green and grue causal variables. Synthese, 193:1029–1046, 2016. (Cited on page 8.) Frederick Eberhardt, Clark Glymour, and Richard Scheines. N-1 experiments suffice to determine the causal relations among n variables. Innovations in Machine Learning: Theory and Applications , pages 97–112, 2006. (Cited on page 29.)...

    arXiv 2016

  6. [8]

    Synergies between disentanglement and sparsity: Generalization and identifiability in multi-task learning

    (Cited on page 23.) S´ ebastien Lachapelle, Tristan Deleu, Divyat Mahajan, Ioannis Mitliagkas, Yoshua Bengio, Simon Lacoste-Julien, and Quentin Bertrand. Synergies between disentanglement and sparsity: Generalization and identifiability in multi-task learning. In International Conference on Machine Learning , 2023. (Cited on page 27.) Steffen Lauritzen. L...

    work page 2023

  7. [9]

    Citris: Causal identifiability from temporal intervened sequences

    (Cited on page 23.) Phillip Lippe, Sara Magliacane, Sindy L¨ owe, Yuki M Asano, Taco Cohen, and Stratis Gavves. Citris: Causal identifiability from temporal intervened sequences. In Interna- tional Conference on Machine Learning , 2022. (Cited on page 23.) Joshua Loftus. Position: The causal revolution needs scientific pragmatism. InInternational Conferen...

    arXiv 2022

  8. [11]

    O O ∈ A denotes the action corresponding to the observational regime, see Definition 2.3

    (Cited on page 23.) 41 A Notation Symbol Description A A set of actions, see Definition 2.3. O O ∈ A denotes the action corresponding to the observational regime, see Definition 2.3. G Directed acyclic graph over nodes {1, . . . , n}. [n] The set {1, . . . , n}. C , A , H Causal Bayesian networks (CBNs), see Definition 2.1. h Function Rm → Rn transforming...

    work page

Show all 22 references
  1. [14]

    That is, IntM satisfies D0 (correct conditionals on intervened nodes)

    La(Z ∗ i | P A∗ i ) ∼ qi for all i ∈ J. That is, IntM satisfies D0 (correct conditionals on intervened nodes)

  2. [15]

    Intuitively, we do not intervene on nodes not in J

    La(Z ∗ i | P A∗ i ) ∼ pC i for all i /∈ J. Intuitively, we do not intervene on nodes not in J. ◦ The M in IntM is for ‘Markov’. Interpretation IntM is the same as IntC except that we do not require that La(Z ∗) is Markov w.r.t. the graph of C for a a to be interpreted as an in...

    2019

  3. [16]

    There exists a surjective function τU : [4] → {0, 1}2 such that τ (M d X (u1)) = M ωτ (d) Y (τU (u1)) for every d ∈ I∗ and u1 ∈ [4]

  4. [18]

    There exists a surjective function τU : R3 → R2 such that τ (M d X (u1, u2, u3)) = M ωτ (d) Y (τU (u1, u2, u3)) for every d ∈ I∗ and (u1, u2, u3) ∈ R3

  5. [19]

    Therefore, we choose IY = ωτ (I ∗) (here, ωτ is defined for all interventions in I ∗)

    The third condition of Definition 3.13 in Beckers and Halpern [2019] would be trivially violated if we chose IY ̸= ωτ (I ∗). Therefore, we choose IY = ωτ (I ∗) (here, ωτ is defined for all interventions in I ∗). Assume for contradiction that ( MY , ωτ (I ∗)) is a τ -abstractio...

    2019

  6. [20]

    This requirement may be overly restrictive as the following example illustrates

    Janzing and Mejia [2024] require that each Aj is nonempty, that is, intuitively, that it is possible to intervene on every node. This requirement may be overly restrictive as the following example illustrates. Assume we are interested in the causal effect of a treatment T ∗ on...

    2024

  7. [21]

    Under IntS, Definition 5.4, we interpret an action a as an intervention d = do(j ← qj) on node j if La(Z ∗ j | P A∗ j ) ∼ qj, La(Z ∗ j | P A∗ j ) ≁ pC j , and La(Z ∗) is Markov w.r.t. the DAG. Therefore, whether d ∈ IntI S(a) depends on both the graph and the specific kernels ...

    2024

  8. [1990]

    What counterfactuals can be tested

    (Cited on page 32.) Ilya Shpitser and Judea Pearl. What counterfactuals can be tested. In Uncertainty in Artificial Intelligence, 2007. (Cited on page 3.) Peter Spirtes and Richard Scheines. Causal inference of ambiguous manipulations. Philos- ophy of Science , 71:833 – 845, 2...

    2007

  9. [2007]

    Commentary: race and sex are causes

    (Cited on page 33.) Clark Glymour and Madelyn R Glymour. Commentary: race and sex are causes. Epi- demiology, 2014. (Cited on page 26.) Limor Gultchin, David Watson, Matt Kusner, and Ricardo Silva. Operationalizing complex causes: A pragmatic view of mediation. In Internationa...

    2014

  10. [2009]

    (Cited on pages 10 and 31.) Sander Beckers and Joseph Y. Halpern. Abstracting causal models. In AAAI Conference on Artificial Intelligence , 2019. (Cited on pages 29, 30, 31, 47, and 48.) Sander Beckers, Frederick Eberhardt, and Joseph Y. Halpern. Approximate causal abstractio...

    2019

  11. [2010]

    Decision-theoretic foundations for statistical causality

    (Cited on page 27.) Philip Dawid. Decision-theoretic foundations for statistical causality. Journal of Causal Inference, 9(1), 2021. (Cited on pages 19 and 26.) Joel Dyer, Nicholas George Bishop, Yorgos Felekis, Fabio Massimo Zennaro, Ani Calinescu, Theodoros Damoulas, and Mic...

    2021

  12. [2020]

    35 Smoke and mirrors in causal downstream tasks

    (Cited on page 24.) Riccardo Cadei, Lukas Lindorfer, Sylvia Cremer, Cordelia Schmid, and Francesco Locatello. 35 Smoke and mirrors in causal downstream tasks. Preprint arXiv:2402.12980, 2024. (Cited on page 27.) Nancy Cartwright. Hunting causes and using them: Approaches in ph...

    2024

  13. [2022]

    Learning linear causal representations from interventions under general nonlinear mixing

    (Cited on page 23.) Simon Buchholz, Goutham Rajendran, Elan Rosenfeld, Bryon Aragam, Bernhard Sch¨ olkopf, and Pradeep Ravikumar. Learning linear causal representations from interventions under general nonlinear mixing. In Advances in Neural Information Processing Systems ,

  14. [2024]

    Invariance, causality and robustness.Statistical Science, 35(3):404–426,

    (Cited on page 23.) Peter B¨ uhlmann. Invariance, causality and robustness.Statistical Science, 35(3):404–426,

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