Writing study: On the Identifiability of Poisson Branching Structural Causal Model Under Latent Confounding

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← ICML 2026 oral writing corpus

Jie Qiao, Zihuai Zeng, Ruichu Cai, Zhengming Chen, Zhifeng Hao · 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

30 physical pages

Before references / appendix

≈ 9.32 page-equivalents

Main figures / tables

6 / 1

Attached appendix figures / tables

4 / 6

Attached appendix span

≈ 18.88 page-equivalents

Before references / appendix: ≈ 31.07%References / intervening material: ≈ 6%Attached appendix: ≈ 62.93%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: Join wrapped printed heading text using adjacent source lines; original heading start coordinates are unchanged.

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	≈ 1.37 pp.	4.57%
2. Latent Confounding Poisson Branching Structural Causal Model	2	≈ 1.6 pp.	5.33%
3. Identifiability	4	≈ 4.32 pp.	14.4%
4. Practical algorithm	8	≈ 0.2 pp.	0.67%
5. Experiments	8	≈ 0.91 pp.	3.03%
6. Conclusion	9	≈ 0.27 pp.	0.9%
Acknowledgments	10	≈ 0.12 pp.	0.4%
Impact Statement	10	≈ 0.16 pp.	0.53%
References	10	≈ 1.79 pp.	5.97%
Appendix	12	≈ 0.6 pp.	2%
A. Closed-Form Solution for PGF of LC-PB-SCM	12	≈ 1.38 pp.	4.6%
B. Proof of Identifiability	14	≈ 11.42 pp.	38.07%
C. Additional Experiments	25	≈ 2.17 pp.	7.23%
D. Additional Discussion of Complexity	27	≈ 0.14 pp.	0.47%
E. Additional Discussion of Robustness	27	≈ 1.27 pp.	4.23%
F. Additional Discussion of Binomial Thinning in the Presence of Latent Variables	29	≈ 1.91 pp.	6.37%

All detected figure and table locations

Main text

• Figure 1 · p. 1
• Figure 2 · p. 5
• Figure 3 · p. 7
• Figure 4 · p. 9
• Figure 5 · p. 9
• Table 1 · p. 9
• Figure 6 · p. 9

Attached appendix

• Figure 7 · p. 19
• Figure 8 · p. 20
• Figure 9 · p. 25
• Table 2 · p. 26
• Table 3 · p. 27
• Table 4 · p. 27
• Figure 10 · p. 27
• Table 5 · p. 28
• Table 6 · p. 28
• Table 7 · p. 28

Argument and organization

1. 1 Introduction; 2 Model and Preliminaries

   Defines branching counts, exogenous latent roots and the partial-graph recovery target.

2. 3 Identifiability

   Uses a motivating asymmetry, Trie representation and local monomial rules to state completeness.

3. 4 Algorithm; 5 Experiments; 6 Conclusion

   Translates algebraic signatures into empirical derivative tests and evaluates finite-sample examples.

Problem, claim and contribution

The paper explicitly excludes intermediate latent mediators and targets an equivalence-class graph rather than the full latent DAG.

Problem formulation and Goal, p.3 · Main paper

Argument and section order

A worked pair of graphs reveals the distinguishing monomial before the general representation theorem and rule family are introduced.

Sections 3.1-3.3, pp.4-6 · Main paper

Figures, captions and visual explanation

The construction diagram links colored graph vertices, pruned paths and algebraic terms; the rule atlas highlights target edges in blue and prints the theorem and monomial condition above each case.

Figure 2, p.5; Figure 3, p.7 · Main paper

Tables, comparisons and evidence

The completeness claim is explicitly for local three-node structures under monomial equivalence, while the algorithm must estimate noisy higher-order derivatives.

Theorem 3.13 and Section 4, p.8 · Main paper

Appendix and reproducibility

The larger-graph results retain low-sample losses to FCI, and the football illustration discloses use of a supplied skeleton rather than end-to-end graph discovery.

Appendix C.2 and Tables 3-4, p.27; robustness example, p.28 · Main paper

Clarity and writing conventions

The main text distinguishes local zero-setting from latent marginalization at one, helping prevent two mathematically different operations from being conflated.

Definitions 2.4-2.5 and Property 2.6, p.4 · Main paper

What to reuse—and what not to infer

Transferable lesson: Turn a family of identification rules into a visual atlas while keeping local completeness, global reconstruction and noisy estimation as separate claims.

Boundary: The guarantee depends on Poisson branching, independent latent roots and stated graph assumptions; local monomial completeness is not unrestricted global identifiability.

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, 8, 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 13, 27, 28. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.

Visually inspected PDF pages

5, 7

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 · 30 pages