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Discrimination, Calibration, and Ranking: A Unified Matrix Framework — arXiv:2611.02215

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.02215
License (as archived): CC0-1.0
Archived: 2026-11-03T10:28:06.710Z
SHA-256 of the archived text: 2a63097b38348a53f9b92bb9b78cb0b52a261a3bb2a0b60a4d717cc8a7c2ca04
Stable URL of this page: https://metraipolis.com/documento/dc_604c689d06bb

How to cite

Discrimination, Calibration, and Ranking: A Unified Matrix Framework — arXiv:2611.02215 — arXiv (en), https://arxiv.org/abs/2611.02215 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_604c689d06bb (Metraipolis archive dc_604c689d06bb, sha256 2a63097b38348a53f9b92bb9b78cb0b52a261a3bb2a0b60a4d717cc8a7c2ca04)

BibTeX

@misc{dc604c689d06bb,
  title = {Discrimination, Calibration, and Ranking: A Unified Matrix Framework — arXiv:2611.02215},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.02215},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_604c689d06bb; sha256 2a63097b38348a53f9b92bb9b78cb0b52a261a3bb2a0b60a4d717cc8a7c2ca04},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.02215. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Discrimination, calibration, and ranking are the three pillars of classifier evaluation, yet no single algebraic language spans all three. A recent indicator-matrix account unifies discrimination measures (precision, recall, F1, Matthews correlation) across binary, multiclass, multilabel and related settings, using Boolean cell operations on indicator label matrices, generalised to soft labels by t-norms. Calibration measures (Brier score, log-loss) and ranking measures (nDCG, AUC) fall outside it. We close the gap with two further classes of cell operators: deviation operators phi(y - yhat), which give a Calibration Framework, and rank- and slice-dependent operators (positional gains for DCG, column concordance cells for AUC), which give a Ranking Framework. Both inherit the micro/macro/exemplar aggregation architecture. For calibration, the three Brier aggregations collapse to one scalar; the Murphy decomposition holds in matrix form (unbinned, binned and isotonic); and, within the Brier-type class-indexed family, a measure is skew-invariant if and only if it depends only on the class-conditional errors alpha_j and beta_j, the calibration analogues of recall and specificity. For ranking, raw DCG collapses across aggregations while nDCG does not; per-class nDCG and per-class AUC are related by a row-column duality; micro-AUC differs from pooled ROC-AUC; raw positional scores are never strictly proper, and nDCG and AUC need not be proper. The skew-invariant per-class building blocks share one class-conditional expectation template. Experiments on two multilabel benchmarks illustrate the distinctions. Many of the results are machine-checked in Lean 4; the proofs, the experiments and the this http URL package are public: this https URL

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.AI, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2611.02215 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T10:19:50.161Z dalla pagina https://arxiv.org/list/cs.AI/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).