mlsanityData to 7 Oct 2026

On Classification-Calibration of Gamma-Phi Losses

arXiv 2302.07321 ↗First posted 14 Feb 2023stat.ML cs.LGcited by 6

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Abstract (arXiv)

Gamma-Phi losses constitute a family of multiclass classification loss functions that generalize the logistic and other common losses, and have found application in the boosting literature. We establish the first general sufficient condition for the classification-calibration (CC) of such losses. To our knowledge, this sufficient condition gives the first family of nonconvex multiclass surrogate losses for which CC has been fully justified. In addition, we show that a previously proposed sufficient condition is in fact not sufficient. This contribution highlights a technical issue that is important in the study of multiclass CC but has been neglected in prior work.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 10 of its 29 references that are in the map. First posted on arXiv 14 Feb 2023.

Builds on

10 of 29 references.

References · 10

  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  2. 2019Robust Bi-Tempered Logistic Loss Based on Bregman Divergencescited by 61
  3. 2021Calibration and Consistency of Adversarial Surrogate Lossescited by 47
  4. 2014Convex Calibration Dimension for Multiclass Loss Matricescited by 21
  5. 2019An Embedding Framework for Consistent Polyhedral Surrogatescited by 21
  6. 2016Multiclass Classification Calibration Functionscited by 13
  7. 2020Weston-Watkins Hinge Loss and Ordered Partitionscited by 9
  8. 2017Online Multiclass Boostingcited by 7
  9. 2022Astral Space: Convex Analysis at Infinitycited by 6
  10. 2022Online Agnostic Multiclass Boostingcited by 3

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Cited by year

Citing papers per year: 2023: 1; 2024: 3; 2025: 2.

6 papers.

  1. 2023Cross-Entropy Loss Functions: Theoretical Analysis and Applicationscited by 206
  2. 2024H-Consistency Guarantees for Regressioncited by 21
  3. 2024Enhanced H-Consistency Boundscited by 18
  4. 2025Adversarial Robustness in Two-Stage Learning-to-Defer: Algorithms and Guaranteescited by 16
  5. 2025Establishing Linear Surrogate Regret Bounds for Convex Smooth Losses via Convolutional Fenchel-Young Lossescited by 2
  6. 2024EnsLoss: Stochastic Calibrated Loss Ensembles for Preventing Overfitting in Classificationcited by 1