Classifier Calibration: With Application to Threat Scores in Cybersecurity
Bibliographic record
Abstract
This article explores the calibration of a classifier output score in binary classification problems. A calibrator is a function that maps the arbitrary classifier score, of a testing observation, onto [0,1] to provide an estimate for the posterior probability of belonging to one of the two classes. Calibration is important for two reasons; first, it provides a meaningful score, that is the posterior probability; second, it puts the scores of different classifiers on the same scale for comparable interpretation. The article presents three main contributions: (1) Introducing multi-score calibration, when more than one classifier provides a score for a single observation. (2) Introducing the exact analogy between two scenarios: (a) designing a classifier from a set of features, and (b) designing a calibrator, to generate a single calibrated score, from a set of scores of different classifiers. Hence, we propose expanding these classifiers’ scores to higher dimensions to boost the calibrator’s performance. (3) Conducting a massive simulation study, in the order of 24,000 experiments, that incorporates different configurations, in addition to experimenting on three real datasets from the cybersecurity domain. The results show that there is no overall winner among the different calibrators and different configurations. However, general advices for practitioners include the following: the Platt’s calibrator (J. Plattet al., 1999), a version of the logistic regression that decreases bias for a small sample size, has a very stable and acceptable performance among all experiments; our suggested multi-score calibration provides better performance than single score calibration in the majority of experiments, including the two real datasets. In addition, expanding the scores can help in some experiments.
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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 | 0.024 | 0.129 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.004 | 0.007 |
| 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".