Writing study: Exact Functional ANOVA Decomposition for Categorical Inputs Models

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← ICML 2026 oral writing corpus

Baptiste Ferrere, Nicolas Bousquet, Fabrice Gamboa, Jean-Michel Loubes, Joseph Muré · 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

18 physical pages

Before references / appendix

≈ 9.13 page-equivalents

Main figures / tables

3 / 7

Attached appendix figures / tables

0 / 1

Attached appendix span

≈ 6.91 page-equivalents

Before references / appendix: ≈ 50.72%References / intervening material: ≈ 10.89%Attached appendix: ≈ 38.39%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	≈ 1.06 pp.	5.89%
2. Background	2	≈ 0.93 pp.	5.17%
3. Main Theoretical Contribution	3	≈ 1.94 pp.	10.78%
4. Computing the Decomposition	5	≈ 1.53 pp.	8.5%
5. Experiments	6	≈ 2.52 pp.	14%
6. Discussion	9	≈ 0.53 pp.	2.94%
Acknowledgements	9	≈ 0.22 pp.	1.22%
Impact Statement	10	≈ 0.09 pp.	0.5%
References	10	≈ 1.95 pp.	10.83%
Appendices	12	≈ 0.03 pp.	0.17%
A. Proofs	12	≈ 4.37 pp.	24.28%
B. Experiments Details	16	≈ 0.97 pp.	5.39%
C. Comparison with TreeHFD	17	≈ 1.55 pp.	8.61%

All detected figure and table locations

Main text

• Figure 1 · p. 3
• Table 1 · p. 7
• Table 2 · p. 7
• Table 3 · p. 7
• Table 4 · p. 7
• Figure 2 · p. 7
• Table 5 · p. 8
• Table 6 · p. 8
• Figure 3 · p. 8
• Table 7 · p. 9

Attached appendix

• Table 8 · p. 17

Argument and organization

1. 1 Introduction; 2 Background

   Defines categorical dependence as the gap in additive explanation.

2. 3 Theoretical Contribution; 4 Computing the Decomposition

   Separates representation, linear-system formulation, basis selection and practical truncation.

3. 5 Experiments; 6 Discussion

   Uses analytical and independent-setting checks before sparse high-dimensional examples and identifiability limits.

Problem, claim and contribution

The title and abstract emphasize exact decomposition, while the computation section carefully distinguishes exact recovery from budgeted low-rank approximation.

Abstract, p.1; Section 4, pp.5-6 · Main paper

Argument and section order

The transition from an overcomplete representation to a selected basis explicitly introduces non-uniqueness before the algorithm.

Section 4, pp.5-6 · Main paper

Figures, captions and visual explanation

The attribution triptych distinguishes signed contribution from absolute importance and states the target class; the final compact table keeps rank, runtime and reconstruction error together.

Figure 1, p.3; Table 7, p.9 · Main paper

Tables, comparisons and evidence

The independent-setting comparison is labeled a sanity check; the high-dimensional example reports less-than-perfect reconstruction and discloses spatially guided subset selection.

Section 5, pp.7,9 · Main paper

Appendix and reproducibility

The proof begins with a three-lemma roadmap; experimental details identify black-box models and a separate comparison is constructed where the competing method’s assumptions hold.

Appendices A.1, B and C, pp.12,16-17 · Main paper

Clarity and writing conventions

The discussion separates computational cost from the conceptually distinct non-identifiability induced by sparse support.

Limitations and Future Work, p.9 · Main paper

What to reuse—and what not to infer

Transferable lesson: Separate existence and exactness from computational tractability and identifiability, then label approximation evidence explicitly.

Boundary: Exact theoretical representation does not make every displayed high-dimensional explanation exact or uniquely determined; no proof verification was performed.

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, 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 12, 16, 17. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.

Visually inspected PDF pages

3, 9

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 · 18 pages