The Matthews correlation coefficient (MCC) is more reliable than balanced accuracy, bookmaker informedness, and markedness in two-class confusion matrix evaluation
Why this work is in the frame
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Bibliographic record
Abstract
Abstract Evaluating binary classifications is a pivotal task in statistics and machine learning, because it can influence decisions in multiple areas, including for example prognosis or therapies of patients in critical conditions. The scientific community has not agreed on a general-purpose statistical indicator for evaluating two-class confusion matrices (having true positives, true negatives, false positives, and false negatives) yet, even if advantages of the Matthews correlation coefficient (MCC) over accuracy and F 1 score have already been shown.In this manuscript, we reaffirm that MCC is a robust metric that summarizes the classifier performance in a single value, if positive and negative cases are of equal importance. We compare MCC to other metrics which value positive and negative cases equally: balanced accuracy (BA), bookmaker informedness (BM), and markedness (MK). We explain the mathematical relationships between MCC and these indicators, then show some use cases and a bioinformatics scenario where these metrics disagree and where MCC generates a more informative response.Additionally, we describe three exceptions where BM can be more appropriate: analyzing classifications where dataset prevalence is unrepresentative, comparing classifiers on different datasets, and assessing the random guessing level of a classifier. Except in these cases, we believe that MCC is the most informative among the single metrics discussed, and suggest it as standard measure for scientists of all fields. A Matthews correlation coefficient close to +1, in fact, means having high values for all the other confusion matrix metrics. The same cannot be said for balanced accuracy, markedness, bookmaker informedness, accuracy and F 1 score.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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