Writing study: Mixtures Closest To A Given Measure: A Semidefinite Programming Approach

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← ICML 2026 oral writing corpus

Srecko Durasinovic, Jean B. Lasserre, Victor Magron · 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

23 physical pages

Before references / appendix

≈ 8.19 page-equivalents

Main figures / tables

4 / 0

Attached appendix figures / tables

0 / 1

Attached appendix span

≈ 10.91 page-equivalents

Before references / appendix: ≈ 35.61%References / intervening material: ≈ 16.96%Attached appendix: ≈ 47.43%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	≈ 2.2 pp.	9.57%
2. Problem Formulation	3	≈ 0.79 pp.	3.43%
3. SDP relaxations: Main properties	4	≈ 2.71 pp.	11.78%
4. Experimental results	7	≈ 0.83 pp.	3.61%
5. Conclusion and Future Work	7	≈ 1.17 pp.	5.09%
Impact Statement	9	≈ 0.05 pp.	0.22%
Acknowledgments	9	≈ 0.1 pp.	0.43%
References	9	≈ 3.89 pp.	16.91%
A. Theoretical guarantees	13	≈ 8.41 pp.	36.57%
B. Handling high-dimensional data	21	≈ 1.34 pp.	5.83%
C. Experimental setup	22	≈ 1.16 pp.	5.04%

All detected figure and table locations

Main text

• Figure 1 · p. 5
• Figure 2 · p. 7
• Figure 3 · p. 8
• Figure 4 · p. 8

Attached appendix

• Table 1 · p. 22

Argument and organization

1. Problem and contribution

   Separates estimating mixture order from assuming it fixed, and specifies a measure accessed through moments rather than an arbitrary black-box dataset claim.

2. Argument sequence

   Problem and moment assumptions precede parallel Wasserstein and TV constructions; a separate extraction algorithm bridges relaxations to clustering initialization.

3. Evidence and verification

   The finite-convergence claim carries a flat-extension rank condition; the discussion explicitly bounds scalability and the precision of low-order relaxations.

Problem, claim and contribution

Separates estimating mixture order from assuming it fixed, and specifies a measure accessed through moments rather than an arbitrary black-box dataset claim.

Contribution statement, p. 2 · Main paper

Argument and section order

Problem and moment assumptions precede parallel Wasserstein and TV constructions; a separate extraction algorithm bridges relaxations to clustering initialization.

Sections 2-3.3, pp. 3-6 · Main paper

Figures, captions and visual explanation

The pipeline labels intermediate infinite-dimensional stages intractable and the relaxation tractable. Iteration plots disclose sorting, random-initialization repetitions, standard-deviation bands and extra SDP cost.

Figure 1, p. 5; Figures 3-4, p. 8; both PNGs inspected · Main paper

Tables, comparisons and evidence

The finite-convergence claim carries a flat-extension rank condition; the discussion explicitly bounds scalability and the precision of low-order relaxations.

Theorem 3.1, p. 5; concluding discussion, p. 8 · Main paper

Appendix and reproducibility

Family-specific moment arguments support the assumptions, while setup gives regularization and numerical rank tolerances and publishes recovered component parameters.

Appendix A.2-A.3, pp. 14-15; C, pp. 22-23 · Main paper

Clarity and writing conventions

The application is called illustrative, keeping mathematical generality separate from the modest-dimensional empirical demonstrations.

Contribution statement, p. 2; conclusion, p. 8 · Main paper

What to reuse—and what not to infer

Transferable lesson: Make the path from exact formulation to finite relaxation and numerical extraction visible, including the certificate and tolerance choices.

Boundary: Fewer downstream iterations are not total-runtime savings without SDP cost; numerical rank tolerance is not an exact certificate, and finite empirical moments add estimation error.

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-focused distributed manuscript scan, not exhaustive technical/proof validation. Sections 1-4 and concluding discussion, pp. 1-8: approximation problem, moment assumptions, Wasserstein/TV relaxations, extraction and illustrative clustering.

Appendix / supplement

Writing-focused appendix scan; code, data and external assets not executed. Appendices A-C, pp. 13-23: duality and family-specific proofs, extraction, both distance cases, high-dimensional approximations and exact experiment settings.

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 ICML 2026 proceedings PDF, PMLR volume 306; retrieved 2026-10-07. Public OpenReview decision notes were not independently reverified. · 23 pages