Estimation Efficiency Under Privacy Constraints
Bibliographic record
Abstract
We investigate the problem of estimating a random variable Y under a privacy constraint dictated by another correlated random variable X. When X and Y are discrete, we express the underlying privacy-utility tradeoff in terms of the privacy-constrained guessing probability (PXY, ε), and the maximum probability Pc(Y|Z) of correctly guessing Y given an auxiliary random variable Z, where the maximization is taken over all PZ|Yensuring that Pc(X|Z) ≤ ε for a given privacy threshold ε ≥ 0. We prove that ħ (PXY, ·) is concave and piecewise linear, which allows us to derive its expression in closed form for any ε when X and Y are binary. In the non-binary case, we derive (PXY, ε) in the high-utility regime (i.e., for sufficiently large, but nontrivial, values of ε) under the assumption that Y and Z have the same alphabets. We also analyze the privacy-constrained guessing probability for two scenarios in which X, Y, and Z are binary vectors. When X and Y are continuous random variables, we formulate the corresponding privacy-utility tradeoff in terms of sENSR(PXY, ε), the smallest normalized minimum mean squared-error (mmse) incurred in estimating Y from a Gaussian perturbation Z. Here, the minimization is taken over a family of Gaussian perturbations Z for which the mmse of f (X) given Z is within a factor 1-ε from the variance of f (X) for any non-constant real-valued function f . We derive tight upper and lower bounds for sENSR when Y is Gaussian. For general absolutely continuous random variables, we obtain a tight lower bound for sENSR(PXY, ε) in the high privacy regime, i.e., for small ε.
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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 | 0.021 | 0.117 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.002 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.005 | 0.012 |
| Open science | 0.004 | 0.006 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.005 | 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".