Bibliographic record
Abstract
We investigate the contraction properties of locally differentially private mechanisms. More specifically, we derive tight upper bounds on the divergence between Pand Qoutput distributions of an -LDP mechanism in terms of a divergence between the corresponding input distributions P and Q, respectively. Our first main technical result presents a sharp upper bound on the χ2-divergence χ2(P||Q) in terms of χ2(P||Q) and . We also show that the same result holds for a large family of divergences, including KL-divergence and squared Hellinger distance. The second main technical result gives an upper bound on χ2(P||Q) in terms of total variation distance (P,Q) and . We then utilize these bounds to establish locally private versions of the van Trees inequality, Le Cam’s, Assouad’s, and the mutual information methods —powerful tools for bounding minimax estimation risks. These results are shown to lead to tighter privacy analyses than the state-of-the-arts in several statistical problems such as entropy and discrete distribution estimation, non-parametric density estimation, and hypothesis testing.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.017 | 0.077 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.004 | 0.014 |
| Open science | 0.005 | 0.010 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".