Selecting fitted models under epistemic uncertainty using a stochastic process on quantile functions
Bibliographic record
Abstract
Fitting models to data is an important part of the practice of science. Advances in machine learning have made it possible to fit more-and more complex-models, but have also exacerbated a problem: when multiple models fit the data equally well, which one(s) should we pick? The answer depends entirely on the modelling goal. In the scientific context, the essential goal is replicability: if a model works well to describe one experiment, it should continue to do so when that experiment is replicated tomorrow, or in another laboratory. The selection criterion must therefore be robust to the variations inherent to the replication process. In this work we develop a nonparametric method for estimating uncertainty on a model's empirical risk when replications are non-stationary, thus ensuring that a model is only rejected when another is reproducibly better. We illustrate the method with two examples: one a more classical setting, where the models are structurally distinct, and a machine learning-inspired setting, where they differ only in the value of their parameters. We show how, in this context of replicability or "epistemic uncertainty", it compares favourably to existing model selection criteria, and has more satisfactory behaviour with large experimental datasets.
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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 | 0.045 | 0.138 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 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; 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".