The sample complexity of agnostic learning under deterministic labels
Bibliographic record
Abstract
With the emergence of Machine Learning tools that allow handling data with a huge number of features, it becomes reasonable to assume that, over the full set of features, the true labeling is (almost) fully determined. That is, the labeling function is deterministic, but not necessarily a member of some known hypothesis class. However, agnostic learning of deterministic labels has so far received little research attention. We investigate this setting and show that it displays a behavior that is quite different from that of the fundamental results of the common (PAC) learning setups. First, we show that the sample complexity of learning a binary hypothesis class (with respect to deterministic labeling functions) is not fully determined by the VC-dimension of the class. For any d, we present classes of VC-dimension d that are learnable from ~ O(d= )many samples and classes that require samples of size ( d= 2 ). Furthermore, we show that in this setup, there are classes for which any proper learner has suboptimal sample complexity. While the class can be learned with sample complexity ~ O(d= ), any proper (and therefore, any ERM) algorithm requires ( d= 2 ) samples. We provide combinatorial characterizations of both phenomena, and further analyze the utility of unlabeled samples in this setting. Lastly, we discuss the error rates of nearest neighbor algorithms under deterministic labels and additional niceness-of-data assumptions.
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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 | 0.013 | 0.084 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.010 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.003 | 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".