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A variational Bayesian model over extended factor graphs can scale causal discovery to thousands of nodes, handle unknown interventions, and recover the true causal graph up to an intervention-specific equivalence class.

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2026-08-01 04:05 UTC pith:QADXQQFR

load-bearing objection Promising method and extensive experiments, but the main identifiability theorem is formally vacuous as stated because the parametric family in Def B.12 is not intervention-dependent; fix that before trusting the guarantees. the 3 major comments →

arxiv 2607.22934 v1 pith:QADXQQFR submitted 2026-07-24 stat.ML cs.LGq-bio.MN

Amortized Bayesian Causal Discovery of Extended Factor Graphs

Yichen Gu , Yuxuan Song , Weizhou Qian , Yixin Wang , Joshua Welch This is my paper
classification stat.ML cs.LGq-bio.MN
keywords causal discoveryfactor graphsvariational inferenceinterventional dataunknown intervention targetsacyclicityidentifiabilitysingle-cell perturbation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

ABCDEFG attacks the combination of scalability, acyclicity, unknown intervention targets, and identifiability that no single existing causal-discovery method handles. The proposal is to represent causal structure as an extended factor graph, sample graphs from a generative process that is acyclic by construction, and fit the posterior via a VAE-style ELBO. The paper's central theoretical claim is that the MAP estimate of the optimized posterior is I-Markov equivalent to the true DAG under four standard assumptions, with a further theorem identifying the underlying factor graph up to permutation for a restricted class of f-DAGs. Empirical results show the method outperforming score-based and Bayesian baselines on simulated data and recovering known and novel growth-factor targets in a single-cell screen. A sympathetic reader would care because this is a rare demonstration of a Bayesian causal-discovery method operating at thousand-node scale with interventional data.

Core claim

On its own terms, the paper's central discovery is that the ELBO-optimal variational posterior over extended factor graphs has a MAP estimate that is I*-Markov equivalent to the true causal DAG (Theorem 2.5), and that within the identifiable f-DAG class G_m the underlying factor graph is recoverable up to factor permutation (Theorem 2.13). This transfers score-based identifiability into a Bayesian setting and makes acyclicity a construction property rather than a constraint.

What carries the argument

The carrying object is the extended factor graph: a DAG whose vertices are n feature nodes, n_I intervention nodes, and m latent factor nodes, with edges only from nodes to factors or factors to nodes. The causal graph is the half-square node graph, i.e. a Boolean product of node-to-factor and factor-to-node matrices; intervention edges enter through an intervention-to-factor matrix. Acyclicity is guaranteed by ordering factors and assigning each node to a partition between consecutive factors. The proof machinery is the Bayesian score function L(q) = E_q[S_I*(G)] - beta*KL(q||p(G)), which connects the ELBO to the score S_I*(G) used in score-based causal discovery.

Load-bearing premise

The chain of guarantees rests on the assumption that the neural encoder/decoder can represent the true interventional distributions exactly, and that the true graph lies in a restricted class of low-rank factorizations whose conditions are not checkable from data.

What would settle it

Run ABCDEFG on a ground-truth graph that violates one of the three identifiable-f-DAG conditions in Definition 2.7—for instance, a factor with no unique parent or child—with ample data and a large encoder, and test whether the MAP f-DAG is I-Markov equivalent to the truth up to permutation; failure would refute Theorem 2.13. For Theorem 2.5, construct a small known DAG whose interventional conditionals cannot be represented by the feed-forward encoder, then check whether the MAP graph is still I-Markov equivalent; if not, Assumption 1 is the load-bearing failure.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If Theorem 2.5 holds, optimizing the ELBO yields a posterior whose MAP graph is I-Markov equivalent to the true DAG, giving a Bayesian counterpart to score-based identifiability results.
  • Because graph samples are acyclic by construction, downstream users skip the pruning step that score-based methods need after thresholding.
  • Jointly modeling unknown intervention targets means the method can infer both the regulatory graph and which genes a drug or growth factor acts through, in one pass.
  • The SPN variant models correlations among edge probabilities, which the paper shows is necessary for accuracy on SPN-simulated nonlinear data.
  • On the 31k-cell growth-factor screen, the method recovers known Gene Ontology targets at recall 0.325-0.376 versus 0.196 for random factor graphs, and reconstructs held-out interventions with lower MSE than baselines.

Where Pith is reading between the lines

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

  • If the sufficient-capacity assumption is not met by the finite encoder/decoder, the practical guarantee becomes heuristic; a natural test is to measure calibration and graph-recovery error as encoder width grows on a known ground-truth graph.
  • The identifiable-f-DAG conditions imply the method will be most reliable when biological modules have unique marker genes and clear separations; pathways with overlapping or shared factors would be expected to merge in the recovered factor graph.
  • Because the framework separates factors as latent modules, the learned factors could serve as hypotheses about pathway structure; one could test this by checking whether factor membership predicts independent perturbation-response measurements not used in training.
  • The authors note real gene-regulatory networks contain cycles; extending the generative process to cyclic graphs would require relaxing the construction, and the identifiability theorem would need a new equivalence notion.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper introduces ABCDEFG, a variational Bayesian method for causal discovery from interventional data. It represents causal structures as extended factor DAGs with intervention nodes, uses Gumbel-softmax or sum-product networks to sample edge matrices that are acyclic by construction, and fits a VAE with causal masks for distributional estimation. The authors prove (Theorem 2.5 / B.15) that the argmax of the ELBO-optimal posterior graph distribution is I*-Markov equivalent to the true graph under assumptions of sufficient capacity, I-faithfulness, positivity, and finite entropy, and (Theorem 2.13 / B.22) that the underlying f-DAG is identifiable up to factor permutation under additional structural conditions. Experiments compare ABCDEFG with score-based and Bayesian baselines on simulated data and on a single-cell growth-factor perturbation screen.

Significance. If the theoretical claims were established, the paper would make a substantial contribution: it combines scalable Bayesian uncertainty quantification with acyclicity-by-construction and unknown intervention targets, and its f-DAG identifiability result would extend the factor-graph line of work. The paper also provides broad empirical evaluation and a detailed appendix. However, the main identifiability theorem currently rests on an internally inconsistent definition of the parametric family, and the proof of the f-DAG identifiability lemma is not at the required level of rigor. The central theoretical guarantee therefore needs substantive correction before the paper can be accepted.

major comments (3)
  1. [Appendix B, Def. B.12 / Eq. (14); Thm 2.5, Assumption 1] Assumption 1 of Theorem 2.5 is unsatisfiable as stated. In Def. B.12 the functions are defined as f^(k)(Z_j|X_pi)=p(f_enc(U_j ⊙ X)) and f^(k)(X_i|Z_pi)=p(f_enc(V_i ⊙ Z)); the right-hand sides do not depend on k. The definition then requires f^(k)(X_i|Z_pi)≠f^(1)(X_i|Z_pi) iff i∈I_k, which is contradictory for any nonempty intervention. Moreover, F_{I*}(D) is a set of joint densities over (X,Z), while the assumption says it contains the marginal interventional distributions p^(k)(X). The intervention mask [U_j⊙X; W^j⊙I] mentioned in §2.5 is absent from Def. B.12, and no argument shows that such a shared encoder yields arbitrary soft/hard interventional conditionals. Consequently Theorem 2.5/B.15 is vacuous as written; the definition of F_{I*} must be corrected and the capacity assumption made precise before the identifiability claim is meaningful.
  2. [Appendix B.2, proof of Theorem B.15] The proof constructs a PMF q' by moving ε mass from \hat G to G*, then argues L(q')>L(q*) contradicts optimality of q*. But the optimization is over q(G;Λ), a restricted parametric family (Gumbel softmax or SPN). The constructed q' is an arbitrary perturbation of q* and is not shown to be representable in that family. Without a representability argument (or a theorem stated for the unconstrained variational family), the contradiction only holds for global optimization over all PMFs, not for the actual ABCDEFG objective. This is a load-bearing gap in the main identifiability proof.
  3. [Theorem 2.13 / Lemma B.18 and Appendix B.3] The f-DAG identifiability result depends on Lemma B.18, which is stated as a sketch in the main text and whose appendix proof is dense and in places not fully justified. For example, the proof of Prop. B.21 repeatedly asserts the existence of factors/nodes with certain properties and concludes a 'v-structure mismatch' without fully verifying all cases; the final step for type-F1 factors says flipping parent/child 'does not introduce v-structure' without considering interactions among multiple F1 factors. Since Theorem 2.13 is a central claimed contribution, the lemma needs a complete, self-contained proof or a precise statement of which parts remain conjectural. The strong conditions in Def. 2.7/D_m should also be clearly flagged as unverifiable structural assumptions, not a general identifiability guarantee.
minor comments (4)
  1. [Section 2.5 / Def. B.12] Please align the theoretical definition with the implemented architecture: the one-hot intervention input [W^j⊙I] appears only in the method description, not in the parametric family used in the theorems. Also clarify whether f^(k)(X|G;Φ) denotes the X-marginal of the joint density or the joint density itself; the current notation switches between the two.
  2. [Abstract / Section 3.2] The abstract claims scaling to 'thousands of nodes,' but the largest simulation has 500 nodes and the real-data experiment uses 1,000 highly variable genes. Please either add a thousand-node experiment or soften the scaling claim.
  3. [Appendix C, Tables 5-6] Several table entries appear garbled (e.g., Table 5 rows for ABCDEFG: '0 0 0120 0 212' and '010 12521 1 26 28 26 22 17 25'). These need to be cleaned so the reported results are readable.
  4. [Section 2.5, unknown-target paragraph] The claim that the unknown-target setting follows by 'replacing the causal DAG with an I-DAG' is not backed by a formal theorem or proof. Please provide a statement or explicitly label this as a heuristic extension.

Circularity Check

0 steps flagged

No circular derivation: identifiability rests on external score-based theorems; the Def. B.12 capacity flaw is a correctness gap, not a circularity.

full rationale

Walking the derivation chain: Theorem 2.5's conclusion is conditional on the external score-identifiability theorem of Brouillard et al. (Theorem B.13), whose assumptions (sufficient capacity, I-faithfulness, positivity, finite entropy) are stated and not derived from the paper's own fitted objects. The Bayesian extension in Theorem B.15 only transfers a small amount of posterior mass to the true graph and invokes the strict inequality SI*(G*) > SI*(Ghat); it does not define the target graph as the maximizer of the fitted quantity. Eq. (19) explicitly notes that for beta=0 and q(G)=delta(G) the objective becomes the existing score, but the paper presents this as a connection, not as the source of its guarantee. Lemma 2.9/Theorem 2.13 are graph-theoretic and proven from Yang et al.'s I-DAG characterization via case analysis on factor partitions; the D_m conditions are sufficient conditions shown by proof, not assumed equivalents. I flag Appendix Def. B.12 as a serious internal inconsistency: the parametric family there has f(k) independent of k, so Assumption 1 of Theorem 2.5 is unsatisfiable for nonempty I*; this makes the theorem vacuous as stated and needs correction, but it is a capacity/expressiveness flaw, not a circular reduction of a prediction to its inputs. Section 4's listed limitations (cycles, high-rank graphs, sample size) are scope caveats, not circular steps. No fitted parameter is renamed as a prediction, and no load-bearing self-citation appears; all cited identifiability results are by other authors. Hence circularity score 0.

Axiom & Free-Parameter Ledger

0 free parameters · 6 axioms · 0 invented entities

ABCDEFG introduces no new physical entity. Its load-bearing nonstandard content is the extended f-DAG representation (intervention nodes feeding factors), the generative sampling process (ordered factors + assignments Y + edge matrix B), and the restrictive D_m class. The main risk is the gap between the D_m identifiability theorem and the unconstrained real-data setting. No free parameters were counted because the L1 coefficients, β, SPN width, and number of factors are standard hyperparameters.

axioms (6)
  • domain assumption Sufficient capacity: the parametric family contains ground-truth interventional distributions (Assumption 1, Theorem 2.5).
    Invoked in the main identifiability theorem; no expressiveness guarantee is given for the specific feed-forward encoder/decoder and Gumbel-softmax or SPN masks.
  • domain assumption I-faithfulness (Appendix B, Thm B.13; Brouillard et al.).
    Imported from DCDI; unverifiable from finite data and required for score separation S_I*(G*) > S_I*(G).
  • domain assumption Causal sufficiency and Markov factorization (Section 2.1, Definition of CGM).
    The causal graphical model assumes no unobserved confounders; stated implicitly in the factorization p(X) = ∏ p(X_i | X_πi).
  • ad hoc to paper The true graph is (or is well-approximated by) an f-DAG with m factors (Section 2.5).
    Load-bearing for the scalable model; the low-rank Boolean factorization assumption is borrowed from Lopez et al. and is acknowledged in the conclusion as a limitation for high-rank graphs.
  • ad hoc to paper The true graph lies in D_m (three conditions: unique parent/child per factor, no adjacent chain/tree, enough v-structures; Def 2.7/B.16).
    This restricted class is the domain of the f-DAG identifiability theorem (Lemma 2.9 / Theorem 2.13). The paper's own Figures 4-6 show the conditions exclude ambiguous graphs, and it is not shown that real biological graphs satisfy them.
  • domain assumption Number of factors m fixed (e.g., 10 factors for 1,000 genes in real data).
    Model capacity and the D_m identifiability result depend on m; no model selection principle for m is given beyond the low-rank rationale.

pith-pipeline@v1.3.0-alltime-deepseek · 36918 in / 10860 out tokens · 86762 ms · 2026-08-01T04:05:01.659775+00:00 · methodology

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read the original abstract

Learning causal graphs from interventional data is a challenging problem with broad applications. In molecular biology, for example, a central goal is to uncover gene regulatory networks from large-scale perturbation data. An ideal algorithm for this task should scale to thousands of nodes, incorporate interventions even when their targets are unknown, quantify uncertainty, and provide identifiability guarantees. However, existing approaches---e.g. approaches using score-based optimization or approximate Bayesian inference---often fail to meet all of these criteria. To address these limitations, we develop Amortized Bayesian Causal Discovery of Extended Factor Graphs (ABCDEFG). Our method guarantees exact acyclicity, scales to graphs with thousands of nodes, and naturally handles interventions even when their targets are unknown. Additionally, ABCDEFG estimates a posterior distribution whose maximum a posteriori estimate provably identifies the true causal graph up to an equivalence class. On simulated datasets, ABCDEFG achieves state-of-the-art accuracy, producing a well-calibrated posterior distribution while outperforming previous score-based and approximate Bayesian methods. Applied to large-scale single-cell perturbation data, ABCDEFG identifies both established and novel gene targets of growth factors.

Figures

Figures reproduced from arXiv: 2607.22934 by Joshua Welch, Weizhou Qian, Yichen Gu, Yixin Wang, Yuxuan Song.

Figure 1
Figure 1. Figure 1: Causal inference using extended factor graphs. (a) Generative process for sampling extended factor graphs that are guaranteed to be acyclic. Factors are ordered to form partitions, then nodes and interventions are inserted into partitions. Finally, edges are added from earlier nodes, factors or interventions to later. Removing factors gives a “half-square” graph with direct node-to-node and intervention-to… view at source ↗
Figure 2
Figure 2. Figure 2: Posterior calibration plot of Bayesian methods and extended factor graph inferred from growth factor screen. (a) 95% confidence intervals estimated empirically (colored regions) across the range of posterior edge probabilities for each method. The black dotted line indicates perfect calibration. (b) Inferred causal edges among interventions with unknown targets (growth factors; pentagons), factors (circles… view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of Sum-Product Network (SPN). (a) Building blocks of an SPN. Top: An input node encodes a PMF or PDF given an input value x. Middle: A product node generates a product of input distributions as the output. Bottom: A sum node generates a mixture of input distributions as the output. (b) An Example of SPN Architecture. Assume inputs are random bits x1 . . . x4. Input nodes generate both 0’s and … view at source ↗
Figure 4
Figure 4. Figure 4: Markov equivalence of DAGs does not imply Markov equivalence of f-DAGs when condition 1 in Def. B.16 is violated. Definition B.17. Let G = (V, E) be a DAG which can be represented as a half-square graph of an f-DAG with m factors. Gm is defined as the set of all DAGs having an identifiable f-DAG representation: Gm := {G : ∃D ∈ Dm, G = D2 [V ]} Now we present the following lemma. Lemma B.18. Let D1 = (V, F,… view at source ↗
Figure 5
Figure 5. Figure 5: Markov equivalence of DAGs does not imply Markov equivalence of f-DAGs when condition 2 in Def. B.16 is violated. First, we prove the forward direction by contradiction. Suppose D1 ≃I D2 but (DI 1 ) 2 [V ] ̸≃I (DI 2 ) 2 [V ]. Then, either there is an edge (i, j) in (DI 1 ) 2 [V ], (i, j) not in (DI 2 ) 2 [V ] or a v￾structure i → k ← j mismatch between (DI 1 ) 2 [V ] and (DI 2 ) 2 [V ]. In the former case,… view at source ↗
Figure 6
Figure 6. Figure 6: Markov equivalence of DAGs does not imply Markov equivalence of f-DAGs when condition 3 in Def. B.16 is violated. Therefore, we conclude that D1 ≃I D2 =⇒ D2 1 [V ] ≃I D2 2 [V ]. Next, we prove the reverse direction. We first claim and prove propositions about the three types of factors. Before presenting the propositions, we repeat important notations here: 1. par(i; D): the set of all parents of node i in… view at source ↗
Figure 7
Figure 7. Figure 7: Illustration of Proposition B.19 (a) Case I: i → j ′ → k in DI 2 . (b) Case II: k → j ′ → i in DI 2 . Contradictory edges are colored red. 31 [PITH_FULL_IMAGE:figures/full_fig_p031_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Illustration of Cases in Proposition B.20 (a) k ∈ chd(j), k /∈ Cj (DI 1 ). (b) Contradictory Case I: ∃k1, k2 ∈ Cj (DI 1 ) s.t. k1 → f1 → i, k2 → f2 → i in DI 2 (c) Contradictory case II: ∃ unique h s.t. h → f ′ → i in DI 2 . (d) Contradictory Case: there exists multiple factors connecting i to chd(j; DI 1 ). (e) Contradictory Case: chd(j; DI ) ⊂ chd(j ′ ; DI 2 ). Proposition B.21. If (DI 1 ) 2 [V ] ≃I (DI … view at source ↗
Figure 9
Figure 9. Figure 9: Illustration of Cases in Case I of Proposition B.21 (a) Subcase I-1. (b) Subcase I-2. (c) Subcase I-3. (d) Subcase I-4. Based on the reasoning above, we have (1) j → Cf ′(DI 2 ) and (2) Pf (DI 2 ) → j in DI 1 . This implies Pf (DI 2 ) → Cf ′ in (DI 1 ) 2 [V ]. Due to the v-structure formed by i, Pf ′(DI 2 ) and Cf ′(DI 2 ) in (DI 2 ) 2 [V ], we also have Pf ′(DI 2 ) → Cf ′(DI 2 ) in (DI 1 ) 2 [V ]. The pre… view at source ↗
Figure 10
Figure 10. Figure 10: Illustration of Cases in Case II of Proposition B.21. (a) Contradictory case when Pj (DI 1 ) ̸⊆ Pf (DI 2 ). (b) Contradictory case when Pj (DI 1 ) ⊆ Pf (DI 2 ) but Pf (DI 2 ) ̸⊆ Pj (DI 1 ). (c) Contradictory case when Cj (DI 1 ) ̸⊆ Cf (DI 2 ). (d) Contradictory case when Cj (DI 1 ) ⊆ Cf (DI 2 ) but Cf (DI 2 ) ̸⊆ Cj (DI 1 ). Because |par(j; DI 1 )| > 1 and |chd(j; DI 1 )| > 1, a v-structure forms ∀i1, i2 ∈… view at source ↗
Figure 11
Figure 11. Figure 11: Overview of ABCDEFG. Top Left: Bayesian framework. A prior p with a support of all DAGs and a variational distribution with a support of f-DAGs. The red star represents the ground-truth DAG and light blue dots with increasing transparency show an optimization process w.r.t. the variational distribution. Top Right: Real vs. generated data distribution. Bottom: ABCDEFG model architecture. Binary matrices U,… view at source ↗
Figure 15
Figure 15. Figure 15: Since the datasets are of similar sizes, the training time is stable across different [PITH_FULL_IMAGE:figures/full_fig_p042_15.png] view at source ↗
Figure 12
Figure 12. Figure 12: Benchmarking of score-based methods on linear datasets. (a) Precision and recall for different score based methods, dataset types are shown in different shapes.(b) SHD comparison between different score based methods on targeted datasets(left two), and untargeted datasets (right two). Appendix D. Preprocessing single cell perturbation data The data used for single cell perturbation is downloaded from Amin… view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of number of acyclic and cyclic graphs [PITH_FULL_IMAGE:figures/full_fig_p044_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Comparison of to be removed number of edges for acyclic graphs. Upper and lower bound of number of to be removed edges are colored in blue and red, respectively. References [1] Abhinav Agrawal, Daniel Sheldon, and Justin Domke. Advances in Black-Box VI: Nor￾malizing flows, importance weighting, and optimization. Neural Information Processing 44 [PITH_FULL_IMAGE:figures/full_fig_p044_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Training Time of ABCDEFG. Each box represents one type of simulation. We group simulation regarding the ground truth graph type and known vs. unknown intervention targets. We use the suffix “-T" for known intervention targets and “-U" for unknown ones. A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 8226–8239. Curran Associates, Inc.… view at source ↗

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Reference graph

Works this paper leans on

31 extracted references · 1 canonical work pages

  1. [1]

    Abhinav Agrawal, Daniel Sheldon, and Justin Domke. Advances in Black-Box VI: Nor- malizing flows, importance weighting, and optimization.Neural Information Processing 44 Amortized Bayesian Causal Discovery of Extended F actor Graphs Table 11: Hyper-Parameter Setting of ABCDEFG in a Simulation Study. Simulation Type L1 Reg. L1 Reg. (Intv.) Activ ation Func...

    2020

  2. [2]

    Amin, Kevin W

    Neal D. Amin, Kevin W. Kelley, Konstantin Kaganovsky, Massimo Onesto, Jin Hao, Yuki Miura, James P. McQueen, Noah Reis, Genta Narazaki, Tommy Li, Shravanti Kulkarni, Sergey Pavlov, and Sergiu P. Pas,ca. Generating human neural diversity with a multiplexed morphogen screen in organoids.Cell Stem Cell, 31(12):1831–1846.e9, 2024. ISSN 1934-5909

    2024

  3. [3]

    Bayesdag: Gradient-based posterior inference for causal discovery.Ad- vances in Neural Information Processing Systems, 36:1738–1763, 2023

    Yashas Annadani, Nick Pawlowski, Joel Jennings, Stefan Bauer, Cheng Zhang, and Wenbo Gong. Bayesdag: Gradient-based posterior inference for causal discovery.Ad- vances in Neural Information Processing Systems, 36:1738–1763, 2023

    2023

  4. [4]

    -T" for known intervention targets and “-U

    Kevin Bello, Bryon Aragam, and Pradeep Ravikumar. Dagma: Learning dags via m-matrices and a log-determinant acyclicity characterization. In S. Koyejo, S. Mohamed, 45 Yichen Gu, Yuxuan Song, Weizhou Qian, Yixin W ang and Joshua Welch Figure 15: Training Time of ABCDEFG.Each box represents one type of simulation. We group simulation regarding the ground tru...

    2022

  5. [5]

    Variational dag estimation via state augmentation with stochastic permutations

    Edwin V Bonilla, Pantelis Elinas, He Zhao, Maurizio Filippone, Vassili Kitsios, and Terry O’Kane. Variational dag estimation via state augmentation with stochastic permutations. arXiv preprint arXiv:2402.02644, 2024

    arXiv 2024

  6. [6]

    Differentiable causal discovery from interventional data.Advances in Neural Information Processing Systems, 33:21865–21877, 2020

    Philippe Brouillard, Sébastien Lachapelle, Alexandre Lacoste, Simon Lacoste-Julien, and Alexandre Drouin. Differentiable causal discovery from interventional data.Advances in Neural Information Processing Systems, 33:21865–21877, 2020

    2020

  7. [7]

    Differentiable DAG sampling

    Bertrand Charpentier, Simon Kibler, and Stephan Günnemann. Differentiable DAG sampling. InInternational Conference on Learning Representations, 2022

    2022

  8. [8]

    iSCAN: Identifying causal mechanism shifts among nonlinear additive noise models

    Tianyu Chen, Kevin Bello, Bryon Aragam, and Pradeep Kumar Ravikumar. iSCAN: Identifying causal mechanism shifts among nonlinear additive noise models. InThirty- seventh Conference on Neural Information Processing Systems, 2023. URL https: //openreview.net/forum?id=GEtXhqKW6X

    2023

  9. [9]

    Bcd nets: Scalable variational approaches for bayesian causal discovery.Advances in Neural Information Processing Systems, 34:7095–7110, 2021

    Chris Cundy, Aditya Grover, and Stefano Ermon. Bcd nets: Scalable variational approaches for bayesian causal discovery.Advances in Neural Information Processing Systems, 34:7095–7110, 2021

    2021

  10. [10]

    Deep end-to-end causal inference

    Tomas Geffner, Javier Antoran, Adam Foster, Wenbo Gong, Chao Ma, Emre Kiciman, Amit Sharma, Angus Lamb, Martin Kukla, Nick Pawlowski, Agrin Hilmkil, Joel Jennings, Meyer Scetbon, Miltiadis Allamanis, and Cheng Zhang. Deep end-to-end causal inference. Transactions on Machine Learning Research, 2024. ISSN 2835-8856

    2024

  11. [11]

    Bacadi: Bayesian causal discovery with unknown 46 Amortized Bayesian Causal Discovery of Extended F actor Graphs interventions

    Alexander Hägele, Jonas Rothfuss, Lars Lorch, Vignesh Ram Somnath, Bernhard Schölkopf, and Andreas Krause. Bacadi: Bayesian causal discovery with unknown 46 Amortized Bayesian Causal Discovery of Extended F actor Graphs interventions. InInternational Conference on Artificial Intelligence and Statistics, pages 1411–1436. PMLR, 2023

    2023

  12. [12]

    Categorical reparameterization with gumbel- softmax

    Eric Jang, Shixiang Gu, and Ben Poole. Categorical reparameterization with gumbel- softmax. InInternational Conference on Learning Representations, 2017

    2017

  13. [13]

    Kingma andMax Welling

    Diederik P. Kingma andMax Welling. Auto-encodingvariational bayes. In YoshuaBengio and Yann LeCun, editors,2nd International Conference on Learning Representations, ICLR 2014, Banff, AB, Canada, April 14-16, 2014, Conference Track Proceedings, 2014

    2014

  14. [14]

    Scaling structural learning with no-bears to infer causal transcriptome networks

    Hao-Chih Lee, Matteo Danieletto, Riccardo Miotto, Sarah T Cherng, and Joel T Dudley. Scaling structural learning with no-bears to infer causal transcriptome networks. In Pacific Symposium on Biocomputing 2020, pages 391–402. World Scientific, 2019

    2020

  15. [15]

    Efficient neural causal discovery without acyclicity constraints

    Phillip Lippe, Taco Cohen, and Efstratios Gavves. Efficient neural causal discovery without acyclicity constraints. InInternational Conference on Learning Representations, 2022

    2022

  16. [16]

    Pritchard, and Aviv Regev

    Romain Lopez, Jan-Christian Hütter, Jonathan K. Pritchard, and Aviv Regev. Large- scale differentiable causal discovery of factor graphs. InAdvances in Neural Information Processing Systems, 2022

    2022

  17. [17]

    Stable differentiable causal discovery

    Achille Nazaret, Justin Hong, Elham Azizi, and David Blei. Stable differentiable causal discovery. In Ruslan Salakhutdinov, Zico Kolter, Katherine Heller, Adrian Weller, Nuria Oliver, Jonathan Scarlett, and Felix Berkenkamp, editors,Proceedings of the 41st International Conference on Machine Learning, volume 235 ofProceedings of Machine Learning Research,...

    2024

  18. [18]

    Structural intervention distance for evaluating causal graphs.Neural Computation, 27(3):771–799, 03 2015

    Jonas Peters and Peter Bühlmann. Structural intervention distance for evaluating causal graphs.Neural Computation, 27(3):771–799, 03 2015. ISSN 0899-7667. doi: 10.1162/NECO_a_00708. URLhttps://doi.org/10.1162/NECO_a_00708

    work page doi:10.1162/neco_a_00708 2015

  19. [19]

    Sum-product networks: A new deep architecture

    Hoifung Poon and Pedro Domingos. Sum-product networks: A new deep architecture. In 2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops), pages 689–690. IEEE, 2011

    2011

  20. [20]

    SoftSort: A continuous relaxation for the argsort operator

    Sebastian Prillo and Julian Eisenschlos. SoftSort: A continuous relaxation for the argsort operator. In Hal Daumé III and Aarti Singh, editors,Proceedings of the 37th International Conference on Machine Learning, volume 119 ofProceedings of Machine Learning Research, pages 7793–7802. PMLR, 13–18 Jul 2020

    2020

  21. [21]

    R. W. Robinson. Counting unlabeled acyclic digraphs. In Charles H. C. Little, editor, Combinatorial Mathematics V, pages 28–43, Berlin, Heidelberg, 1977. Springer Berlin Heidelberg. ISBN 978-3-540-37020-8

    1977

  22. [22]

    Probabilistic circuits for variational inference in discrete graphical models.Advances in neural information processing systems, 33:4635–4646, 2020

    Andy Shih and Stefano Ermon. Probabilistic circuits for variational inference in discrete graphical models.Advances in neural information processing systems, 33:4635–4646, 2020. 47 Yichen Gu, Yuxuan Song, Weizhou Qian, Yixin W ang and Joshua Welch

    2020

  23. [23]

    An algorithm for fast recovery of sparse causal graphs

    Peter Spirtes and Clark Glymour. An algorithm for fast recovery of sparse causal graphs. Social Science Computer Review, 9(1):62–72, 1991

    1991

  24. [24]

    DeepITE: Designing variational graph autoencoders for intervention target estimation

    Hongyuan Tao, Hang Yu, and Jianguo Li. DeepITE: Designing variational graph autoencoders for intervention target estimation. InThe Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. URL https://openreview.net/ forum?id=GMsi9966DR

    2024

  25. [25]

    Prodag: Projection-induced variational inference for directed acyclic graphs.arXiv preprint arXiv:2405.15167, 2024

    Ryan Thompson, Edwin V Bonilla, and Robert Kohn. Prodag: Projection-induced variational inference for directed acyclic graphs.arXiv preprint arXiv:2405.15167, 2024

    arXiv 2024

  26. [26]

    Characterizing and learning equiva- lence classes of causal DAGs under interventions

    Karren Yang, Abigail Katcoff, and Caroline Uhler. Characterizing and learning equiva- lence classes of causal DAGs under interventions. In Jennifer Dy and Andreas Krause, editors,Proceedings of the 35th International Conference on Machine Learning, vol- ume 80 ofProceedings of Machine Learning Research, pages 5541–5550. PMLR, 10–15 Jul 2018

    2018

  27. [27]

    Learning unknown interven- tion targets in structural causal models from heterogeneous data

    Yuqin Yang, Saber Salehkaleybar, and Negar Kiyavash. Learning unknown interven- tion targets in structural causal models from heterogeneous data. In Sanjoy Das- gupta, Stephan Mandt, and Yingzhen Li, editors,Proceedings of The 27th Inter- national Conference on Artificial Intelligence and Statistics, volume 238 ofProceed- ings of Machine Learning Research...

    2024

  28. [28]

    Low-rank regularization for learning gene expression programs.PloS one, 8(12):e82146, 2013

    Guibo Ye, Mengfan Tang, Jian-Feng Cai, Qing Nie, and Xiaohui Xie. Low-rank regularization for learning gene expression programs.PloS one, 8(12):e82146, 2013

    2013

  29. [29]

    Dags with no curl: An efficient dag structure learning approach

    Yue Yu, Tian Gao, Naiyu Yin, and Qiang Ji. Dags with no curl: An efficient dag structure learning approach. In Marina Meila and Tong Zhang, editors,Proceedings of the 38th International Conference on Machine Learning, volume 139 ofProceedings of Machine Learning Research, pages 12156–12166. PMLR, 18–24 Jul 2021

    2021

  30. [30]

    Dags with no tears: Continuous optimization for structure learning

    Xun Zheng, Bryon Aragam, Pradeep K Ravikumar, and Eric P Xing. Dags with no tears: Continuous optimization for structure learning. In S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, editors,Advances in Neural Information Processing Systems, volume 31. Curran Associates, Inc., 2018

    2018

  31. [31]

    Low-rank graph- regularized structured sparse regression for identifying genetic biomarkers.IEEE Trans- actions on Big Data, 3(4):405–414, 2017

    Xiaofeng Zhu, Heung-Il Suk, Heng Huang, and Dinggang Shen. Low-rank graph- regularized structured sparse regression for identifying genetic biomarkers.IEEE Trans- actions on Big Data, 3(4):405–414, 2017. 48

    2017