Writing study: Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks

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← ICLR 2026 oral writing corpus

Songyao Jin, Biwei Huang · Official ICLR 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 foundations (primary) · Learning & optimization algorithms.

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

33 physical pages

Before references / appendix

≈ 9.87 page-equivalents

Main figures / tables

5 / 0

Attached appendix figures / tables

5 / 8

Attached appendix span

≈ 19.9 page-equivalents

Before references / appendix: ≈ 29.91%References / intervening material: ≈ 9.79%Attached appendix: ≈ 60.3%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

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	≈ 0.77 pp.	2.33%
2 RELATED WORK	2	≈ 0.57 pp.	1.73%
3 PARTIALLY OBSERVED MULTIVARIATE HAWKES PROCESS-BASED	2	≈ 0.97 pp.	2.94%
4 STRUCTURE IDENTIFICATION IN PARTIALLY OBSERVED HAWKES	3	≈ 4.89 pp.	14.82%
5 RANK-BASED DISCOVERY ALGORITHM	8	≈ 0.74 pp.	2.24%
6 EXPERIMENTS	9	≈ 0.83 pp.	2.52%
7 CONCLUSION AND FUTURE WORK	10	≈ 0.15 pp.	0.45%
ACKNOWLEDGMENTS	10	≈ 0.09 pp.	0.27%
ETHICS STATEMENT	10	≈ 0.13 pp.	0.39%
REPRODUCIBILITY STATEMENT	10	≈ 0.11 pp.	0.33%
LLM USAGE STATEMENT	10	≈ 0.09 pp.	0.27%
REFERENCES	10	≈ 3.24 pp.	9.82%
Appendix	14	≈ 0.78 pp.	2.36%
A DETAILED RELATED WORK	14	≈ 1.7 pp.	5.15%
B MULTIVARIATE HAWKES PROCESS DETAILS	16	≈ 0.29 pp.	0.88%
C IDENTIFYING INTERMEDIATE LATENT SUBPROCESSES	16	≈ 1.23 pp.	3.73%
D RANK FAITHFULNESS FOR THE HAWKES PROCESS	18	≈ 0.28 pp.	0.85%
E ACCOUNTING FOR SELF-LOOPED OBSERVED SUBPROCESSES UNDER	18	≈ 1.03 pp.	3.12%
F PROOF OF PROPOSITION 3.4	19	≈ 0.18 pp.	0.55%
G PROOF OF THEOREM 4.1	19	≈ 1.51 pp.	4.58%
H PROOF OF LEMMA 4.2	21	≈ 0.38 pp.	1.15%
I PROOF OF PROPOSITION 4.3	21	≈ 0.37 pp.	1.12%
J PRELIMINARIES FOR PROOFS OF PROPOSITION 4.5 AND THEOREMS 4.7	21	≈ 0.57 pp.	1.73%
K PROOF OF PROPOSITION 4.5	22	≈ 1.68 pp.	5.09%
L PROOF OF THEOREM 4.7	24	≈ 0.78 pp.	2.36%
M PROOF OF THEOREM 4.8	24	≈ 0.87 pp.	2.64%
N PROOF OF THEOREM 5.1	25	≈ 0.71 pp.	2.15%
O DETAILS OF IDENTIFICATION ALGORITHM	26	≈ 0.39 pp.	1.18%
P COMPUTATIONAL COMPLEXITY OF THE ALGORITHM	26	≈ 0.82 pp.	2.48%
Q MORE DETAILS OF EXPERIMENTS	27	≈ 6.32 pp.	19.15%

All detected figure and table locations

Main text

• Figure 1 · p. 4
• Figure 2 · p. 5
• Figure 3 · p. 8
• Figure 4 · p. 9
• Figure 5 · p. 10

Attached appendix

• Figure 6 · p. 17
• Figure 7 · p. 18
• Figure 8 · p. 29
• Table 1 · p. 29
• Table 2 · p. 30
• Table 3 · p. 30
• Table 4 · p. 30
• Table 5 · p. 31
• Figure 9 · p. 31
• Table 6 · p. 31
• Table 7 · p. 32
• Figure 10 · p. 32
• Table 8 · p. 32

Argument and organization

1. Event processes to window graphs

   Builds a representation bridge before identification claims.

2. Observed parents to latent surrogates

   Develops rank conditions through progressively harder examples.

3. Alternating discovery and sensitivity tests

   Connects propositions to algorithm phases and practical failure regimes.

Problem, claim and contribution

The introduction distinguishes entirely unobserved event streams from missing timestamps within known streams. This precise gap explains why the method must discover the number and connections of latent subprocesses rather than merely impute events.

§1, pp.1–2 · Main paper

Argument and section order

Four identification results lead directly to the algorithm's two phases. The theorem's scope retains common kernel shape, rank faithfulness and at least two suitable observed surrogates; the headline does not establish recovery of arbitrary hidden networks.

Assumption1, p.6; Theorem5.1 and Algorithm1, p.9 · Main paper

Figures, captions and visual explanation

Figures1–3 reuse observed/latent colors while moving from summary graphs to time-unrolled graphs and increasingly complex latent paths. The counterexamples surrounding symmetric path length make an otherwise dense identification assumption understandable.

Figures1–3 and Definition4.4, pp.4–8 · Main paper

Tables, comparisons and evidence

The real experiment deliberately hides one alarm in a five-alarm, single-device subgraph. The appendix also reports the much poorer merged-device F1 of0.17, versus0.76 on the selected subgraph, showing why homogeneous mechanism assumptions matter.

§6, pp.9–10; AppendixQ.4 and Table8, pp.31–32 · Main paper

Appendix and reproducibility

A contents page navigates seventeen appendices. Useful additions include bin-width and rank-threshold sweeps, a14-subprocess graph, runtime, and a transparent evaluation rule that simplifies ground truth and matches inferred latent nodes rather than comparing raw graphs unchanged.

Appendix contents, p.14; AppendicesP–Q, pp.27–32 · Main paper

Clarity and writing conventions

Proof-reading requires more caution than the prose suggests: AppendixH extends a Gaussian conditional-independence statement to arbitrary noise from second-order information alone. Uncorrelated white noise does not itself establish the required independence equivalence, so this step needs specialist verification.

Lemma4.2, p.5; AppendicesG–H, pp.19–21 · Main paper

What to reuse—and what not to infer

Transferable lesson: Teach a latent-structure theorem through a ladder of graphical examples, then test its assumptions directly and publish the graph-matching rules that determine reported recovery scores.

Boundary: The analysis is conditional on restrictive excitation and path assumptions; finite-bin approximations and estimated covariance ranks introduce additional error. The5k-sample appendix result favors SHP over the proposed method. Reading every supplied proof is not independent proof certification or evidence of intervention-valid real-world causation.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-09-19

Reading status

Full text + selected visuals inspected

Main text

pp.1–10, §§1–7 and declarations; references pp.10–13

Appendix / supplement

pp.14–33, A–Q: related work, all supplied proofs, latent-path examples, algorithms, complexity, synthetic sensitivities and alarm-network analysis

Visually inspected PDF pages

5, 31

• official ICLR 2026 proceedings PDF including appendices A–Q · 33 pages