Writing study: A Recursive Decomposition Framework for Causal Structure Learning in the Presence of Latent Variables

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← ICML 2026 oral writing corpus

Zheng Li, Feng Xie, Shenglan Nie, Xichen Guo, Ruxin Wang, Hao Zhang · Official ICML 2026 oral record

Observed writing choices, not acceptance rules. This study examines the inspected manuscript version. It does not establish why the paper was accepted or that its presentation choices should be copied unchanged.

Figure, table and section ledger

Editorial contribution type: Theory & formal analysis (primary).

Layout extraction, not a required paper template. Counts are distinct caption labels; a multi-panel figure counts once. Section spans are estimated from heading positions, including floats and whitespace. Method and limitations.

Canonical PDF

32 physical pages

Before references / appendix

≈ 9.25 page-equivalents

Main figures / tables

4 / 0

Attached appendix figures / tables

9 / 4

Attached appendix span

≈ 18.91 page-equivalents

Before references / appendix: ≈ 28.91%References / intervening material: ≈ 12%Attached appendix: ≈ 59.09%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: The supporting-material envelope includes the printed Appendix Contents page14 before Appendix A on page15.

Section-by-section lengths and source pages

The title/abstract/front matter precede the first numbered heading. A span ends at the next detected top-level heading, not at the last sentence; end-page whitespace is included. References and statements are listed separately. These are not measurements of text-only or artwork area.

Top-level heading	Starts on PDF page	Estimated span	Share of entire PDF
1. Introduction	1	≈ 1.08 pp.	3.38%
2. Related Work	2	≈ 0.48 pp.	1.5%
3. Preliminaries	2	≈ 0.85 pp.	2.66%
4. Foundations of Recursive Decomposition	3	≈ 0.9 pp.	2.81%
5. Implementation of Recursive Decomposition	4	≈ 2.51 pp.	7.84%
6. Experiments	7	≈ 2.27 pp.	7.09%
7. Conclusions and Discussions	9	≈ 0.62 pp.	1.94%
Acknowledgements	10	≈ 0.11 pp.	0.34%
Impact Statement	10	≈ 0.1 pp.	0.31%
References	10	≈ 3.84 pp.	12%
Appendix Contents	14	≈ 1 pp.	3.13%
A. Detailed Preliminaries	15	≈ 1.48 pp.	4.63%
B. Proofs	16	≈ 4.6 pp.	14.37%
C. Supplementary Experiments	21	≈ 8.92 pp.	27.88%
D. Limitations and Discussion	30	≈ 2.91 pp.	9.09%

All detected figure and table locations

Main text

• Figure 1 · p. 2
• Figure 2 · p. 5
• Figure 3 · p. 8
• Figure 4 · p. 9

Attached appendix

• Table 1 · p. 15
• Table 2 · p. 21
• Figure 5 · p. 22
• Figure 6 · p. 23
• Figure 7 · p. 24
• Figure 8 · p. 25
• Figure 9 · p. 26
• Figure 10 · p. 27
• Figure 11 · p. 28
• Figure 12 · p. 29
• Table 3 · p. 30
• Figure 13 · p. 30
• Table 4 · p. 31

Argument and organization

1. 1 Introduction; 2 Related Work; 3 Preliminaries

   Defines the latent-variable setting and the PAG target before the decomposition question.

2. 4 Foundations; 5 Implementation

   Builds from separation theorems to reconstruction, usable partitions and recursive pseudocode.

3. 6 Experiments; 7 Conclusions and Discussions

   Tests wrappers around five learners and separates a biological illustration from known-graph simulation.

Problem, claim and contribution

The target is an observed-variable equivalence class, not recovery of every hidden variable or a uniquely identified causal DAG.

Problem Setup and Goal, p.3 · Main paper

Argument and section order

Each theorem is followed by an interpretation, and the top-down separation results culminate in a constructive bottom-up merge rule.

Theorems 1-3 and synthesis, p.4 · Main paper

Figures, captions and visual explanation

One graph example is carried through DAG, MAG, PAG, decomposition and merging; the results grid aligns CI-test counts, log runtime and F1 by base learner with red consistently identifying the wrapper.

Figure 2, p.5; Figure 3, p.8 · Main paper

Tables, comparisons and evidence

Soundness assumes an independence oracle and a sound complete base learner; empirical tests instead use finite samples, capped runtime and fifty generated datasets.

Theorem 4, p.6; experimental protocol, p.7 · Main paper

Appendix and reproducibility

The supplement lists CI-test implementation and induced-MAG density, then explains why dense graphs reduce speed benefits without changing the conditional correctness theorem.

Appendix C, p.21; Appendix D.1, p.30 · Main paper

Clarity and writing conventions

The biological application states that its true graph is unknown and interprets pathway agreement as consistency rather than ground-truth causal validation.

Section 6.2, p.9 · Main paper

What to reuse—and what not to infer

Transferable lesson: Use a single worked graph to connect definitions, proof claims and algorithm stages, while separating oracle guarantees from finite-sample behavior.

Boundary: Sparse decomposability drives acceleration; the assumptions include Markovness, faithfulness and no selection bias, and biological plausibility does not verify causal edges.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-10-07

Reading status

Writing-focused manuscript scan + selected visuals inspected

Main text

Writing-oriented scan of the main argument through physical p.9, with focused physical-page text inspection on 1, 3, 4, 5, 6, 7, 9. Framing, section progression, mechanism/proof explanation, displays, comparison conditions and conclusions were inspected. This is not exhaustive technical reading, proof verification or reproduction.

Appendix / supplement

Appendix organization and main-text pointers were checked; focused text inspection of physical pages 21, 30. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.

Visually inspected PDF pages

5, 8

This is a writing-focused scan of the manuscript and the stated supplementary scope: framing, organization, visual explanation, evidence presentation and wording. It is not a line-by-line proof audit, reproduction of results or exhaustive scientific review.

• Published proceedings PDF, PMLR volume 306, retrieved 2026-10-07 · 32 pages