Does Unlabeled Data Provably Help? Worst-case Analysis of the Sample Complexity of Semi-Supervised Learning.
Bibliographic record
Abstract
We study the potential benefits of unlabeled data to classification prediction to the learner. We compare learning in the semi-supervised model to the standard, supervised PAC (distribution free) model, considering both the realizable and the unrealizable (agnostic) settings. Roughly speaking, our conclusion is that access to unlabeled samples cannot provide sample size guarantees that are better than those obtainable without access to unlabeled data, unless one postulates very strong assumptions about the distribution of the labels. In particular, we prove that for basic hypothesis classes over the real line, if the distribution of unlabeled data is ‘smooth’, knowledge of that distribution cannot improve the labeled sample complexity by more than a constant factor (e.g., 2). We conjecture that a similar phenomena holds for any hypothesis class and any unlabeled data distribution. We also discuss the utility of semi-supervised learning under the common cluster assumption concerning the distribution of labels, and show that even in the most accommodating cases, where data is generated by two uni-modal label-homogeneous distributions, common SSL paradigms may be misleading and inflict poor prediction performance.
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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 | 0.049 | 0.244 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.007 | 0.018 |
| Open science | 0.005 | 0.007 |
| Research integrity | 0.004 | 0.008 |
| 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".