Classifier Calibration: With Application to Threat Scores in Cybersecurity
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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. Platt <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 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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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it