Fast and Private Submodular and $k$-Submodular Functions Maximization\n with Matroid Constraints
Bibliographic record
Abstract
The problem of maximizing nonnegative monotone submodular functions under a\ncertain constraint has been intensively studied in the last decade, and a wide\nrange of efficient approximation algorithms have been developed for this\nproblem. Many machine learning problems, including data summarization and\ninfluence maximization, can be naturally modeled as the problem of maximizing\nmonotone submodular functions. However, when such applications involve\nsensitive data about individuals, their privacy concerns should be addressed.\nIn this paper, we study the problem of maximizing monotone submodular functions\nsubject to matroid constraints in the framework of differential privacy. We\nprovide $(1-\\frac{1}{\\mathrm{e}})$-approximation algorithm which improves upon\nthe previous results in terms of approximation guarantee. This is done with an\nalmost cubic number of function evaluations in our algorithm.\n Moreover, we study $k$-submodularity, a natural generalization of\nsubmodularity. We give the first $\\frac{1}{2}$-approximation algorithm that\npreserves differential privacy for maximizing monotone $k$-submodular functions\nsubject to matroid constraints. The approximation ratio is asymptotically tight\nand is obtained with an almost linear number of function evaluations.\n
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.008 | 0.071 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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; both teacher heads agree on what is shown here.
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".