Locally Private Hypothesis Selection
Bibliographic record
Abstract
We initiate the study of hypothesis selection under local differential privacy.\n Given samples from an unknown probability distribution $p$ and a set of $k$ probability distributions $\mathcal{Q}$, we aim to output, under the constraints of $\varepsilon$-differential privacy, a distribution from $\mathcal{Q}$ whose total variation distance to $p$ is comparable to the best such distribution.\n This is a generalization of the classic problem of $k$-wise simple hypothesis testing, which corresponds to when $p \in \mathcal{Q}$, and we wish to identify $p$.\n Absent privacy constraints, this problem requires $O(\log k)$ samples from $p$, and it was recently shown that the same complexity is achievable under (central) differential privacy.\n However, the naive approach to this problem under local differential privacy would require $\tilde O(k^2)$ samples.\n\n We first show that the constraint of local differential privacy incurs an exponential increase in cost: any algorithm for this problem requires at least $\Omega(k)$ samples.\n Second, for the special case of $k$-wise simple hypothesis testing, we provide a non-interactive algorithm which nearly matches this bound, requiring $\tilde O(k)$ samples.\n Finally, we provide sequentially interactive algorithms for the general case, requiring $\tilde O(k)$ samples and only $O(\log \log k)$ rounds of interactivity.\n Our algorithms are achieved through a reduction to maximum selection with adversarial comparators, a problem of independent interest for which we initiate study in the parallel setting.\n For this problem, we provide a family of algorithms for each number of allowed rounds of interaction $t$, as well as lower bounds showing that they are near-optimal for every $t$.\n Notably, our algorithms result in exponential improvements on the round complexity of previous methods.
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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 | 0.011 | 0.045 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.004 | 0.007 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.013 | 0.003 |
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".