Large‐margin classification with multiple decision rules
Bibliographic record
Abstract
Binary classification is a common statistical learning problem in which a model is estimated on a set of covariates for some outcome, indicating the membership of one of two classes. In the literature, there exists a distinction between hard and soft classification. In soft classification, the conditional class probability is modeled as a function of the covariates. In contrast, hard classification methods only target the optimal prediction boundary. While hard and soft classification methods have been studied extensively, not much work has been performed to compare the actual tasks of hard and soft classification. In this paper, we propose a spectrum of statistical learning problems that span the hard and soft classification tasks based on fitting multiple decision rules to the data. By doing so, we reveal a novel collection of learning tasks of increasing complexity. We study the problems using the framework of large‐margin classifiers and a class of piecewise linear convex surrogates, for which we derive statistical properties and a corresponding sub‐gradient descent algorithm. We conclude by applying our approach to simulation settings and a magnetic resonance imaging (MRI) dataset from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study.
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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 | 0.033 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 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".