Interval Selection with Binary Predictions
Bibliographic record
Abstract
Following a line of work that takes advantage of vast machine-learned data to enhance online algorithms with (possibly erroneous) information about future inputs, we consider predictions in the context of deterministic algorithms for the problem of selecting a maximum weight independent set of intervals arriving on the real line. We look at two weight functions, unit (constant) weights, and weights proportional to the interval’s length. In the classical online model of irrevocable decisions, no algorithm can achieve constant competitiveness. In this setting, we show that a simple algorithm that is faithful to the predictions is optimal, and achieves an objective value of at least OPT - η, with η being the total error in the predictions, both for unit, and proportional weights. When revocable acceptances (a form of preemption) are allowed, the optimal deterministic algorithm for unit weights is 2k-competitive, where k is the number of different interval lengths. We give an algorithm with performance OPT − η (and therefore 1-consistent), that is also (2k + 1)-robust. For proportional weights, there is an optimal (2φ + 1)-competitive algorithm, where φ is the golden ratio. We present an algorithm with parameter λ > 1 that is 3λ / (λ - 1) -consistent, and (4λ^2 + 2λ) / (λ - 1)-robust. Although these bounds are not tight, we show that for λ > 3.42 we achieve consistency better than the optimal online guarantee, while maintaining bounded robustness. We conclude with some experimental results on real-world data that complement our theoretical findings, and show the benefit of prediction algorithms for online interval selection, even in the presence of high error.
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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 | 0.004 | 0.023 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".