The effect of finite sample size on the holdout error probability estimator of homoscedastic multi-class Gaussian classification problems
Bibliographic record
Abstract
Consider a homoscedastic multi-class Gaussian classification problem where the class mean vectors and the common covariance matrix are not known to the practitioner. Rather, they are estimated from given sample vectors available for each class. In this paper, an empirical procedure for approximating the bias of the holdout estimator of the Bayesian error probability (BEP) is presented. Synthetic experiments demonstrate the accuracy of the proposed procedure and how it can be used for guiding the practitioner about the necessary amount of data vectors required to achieve a certain level of accuracy in the BEP estimation. When applied to real world classification problems from the UCI machine learning repository, the proposed procedure was successfully used to estimate the test error probability based on the training data only. Moreover, with a reasonable degree of accuracy, the proposed procedure predicted the test BEP when the amount of the training data in increased.
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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 | 0.075 | 0.386 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.001 | 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".