Writing study: Differentially Private Domain Discovery

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← ICLR 2026 oral writing corpus

Vinod Raman, Travis Dick, Matthew Joseph · 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).

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

27 physical pages

Before references / appendix

≈ 9.29 page-equivalents

Main figures / tables

3 / 0

Attached appendix figures / tables

10 / 1

Attached appendix span

≈ 16.34 page-equivalents

Before references / appendix: ≈ 34.41%References / intervening material: ≈ 5.07%Attached appendix: ≈ 60.52%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	≈ 1.07 pp.	3.96%
2 PRELIMINARIES	2	≈ 0.91 pp.	3.37%
3 PRIVATE SET UNION	3	≈ 2.42 pp.	8.96%
4 APPLYING THE WEIGHTED GAUSSIAN MECHANISM	5	≈ 2.5 pp.	9.26%
5 EXPERIMENTS	8	≈ 1.44 pp.	5.33%
6 FUTURE DIRECTIONS	9	≈ 0.48 pp.	1.78%
REFERENCES	10	≈ 1.37 pp.	5.07%
A USEFUL CONCENTRATION INEQUALITIES	11	≈ 0.64 pp.	2.37%
B PRIVACY ANALYSIS OF PEELING EXPONENTIAL MECHANISM	12	≈ 0.14 pp.	0.52%
C MISSING PROOFS	12	≈ 8.77 pp.	32.48%
D LOWER BOUNDS	21	≈ 2.01 pp.	7.44%
E EXPERIMENT DETAILS	23	≈ 1.58 pp.	5.85%
F ADDITIONAL EXPERIMENTAL RESULTS	24	≈ 3.21 pp.	11.89%

All detected figure and table locations

Main text

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

Attached appendix

• Table 1 · p. 23
• Figure 4 · p. 23
• Figure 5 · p. 24
• Figure 6 · p. 24
• Figure 7 · p. 24
• Figure 8 · p. 25
• Figure 9 · p. 25
• Figure 10 · p. 25
• Figure 11 · p. 26
• Figure 12 · p. 26
• Figure 13 · p. 27

Argument and organization

1. Introduction / Related Work / Preliminaries

   Motivates missing mass rather than recovered-item cardinality and defines the privacy setting.

2. Private Set Union

   Uses an impossibility example to motivate assumptions before presenting upper and lower bounds.

3. Applying the Weighted Gaussian Mechanism

   Reuses domain discovery as a composable precursor for two downstream tasks.

4. Experiments / Future Directions / Appendices

   Tests the metric-based argument and exposes remaining theoretical gaps.

Problem, claim and contribution

The contribution is a different utility lens and guarantees for a simple existing mechanism, not a needlessly renamed new algorithm. Frequency-weighted missing mass explains why recovering fewer unique items can still preserve useful data mass.

§1, p.1; Definition 2.2, p.3 · Main paper

Argument and section order

A singleton counterexample precedes the Zipfian condition. The prose explicitly separates this utility assumption from worst-case differential privacy, then distinguishes the distribution-free infinity-norm guarantee used by downstream algorithms.

§3, p.3; Theorem 3.6, p.5 · Main paper

Figures, captions and visual explanation

Aligned three-dataset panels hold the horizontal control variable constant, making trends comparable. Metric direction appears in Figure 1's caption; Figure 2 uses a shared purple method curve against several baseline parameter choices.

Figures 1–2, pp.8–9 · Main paper

Tables, comparisons and evidence

Each experimental subsection repeats Datasets, Baselines and Results lead-ins. The hitting-set comparison explicitly identifies one reference as non-private and another as assuming public domain knowledge, preventing an invalid equal-privacy comparison.

§§5.1–5.3, pp.8–9 · Main paper

Appendix and reproducibility

Named helper lemmas decompose subsampling and thresholding failures; the proofs then assemble their events. Dataset item semantics, rank-frequency plots, item-set distributions and the stricter privacy-budget experiments occupy separate appendices.

Appendices C.2, E–F, pp.13–17, 23–27 · Main paper

Clarity and writing conventions

The conclusion names unmatched upper/lower bounds and uniform subsampling as open directions instead of presenting every result as optimal. This keeps the near-optimal set-union statement separate from unresolved downstream rates.

§6, p.9 · Main paper

What to reuse—and what not to infer

Transferable lesson: Explain why the chosen objective matters, state impossibility and assumptions before guarantees, and label benchmark baselines that operate under stronger information access.

Boundary: The rendered Corollary 4.6 on p.8 prints a greater-than inequality although its lower-bound discussion and Appendix D.3 construct an upper bound on achieved hits. Do not copy the inequality without checking. The conference inventory title differs from the final PDF title; preserve the stable paper ID and version.

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

PDF pp.1–10, §§1–6 and final experiment figure; references pp.10–11

Appendix / supplement

PDF pp.11–27, Appendices A–F: concentration bounds, privacy composition, upper/lower-bound proofs, dataset definitions and additional experiments

Visually inspected PDF pages

8, 9

• official ICLR 2026 proceedings PDF; manuscript title: Missing Mass for Differentially Private Domain Discovery · 27 pages