# Consistent Classification with Generalized Metrics

arXiv: https://arxiv.org/abs/1908.09057 · HTML: https://mlsanity.com/paper/1908.09057/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Aug 2019.

## Built on by (most cited first, 3 of 3)

- [Optimal Binary Classification Beyond Accuracy](https://mlsanity.com/paper/2107.01777/) (2021)
- [Consistent algorithms for multi-label classification with macro-at-k metrics](https://mlsanity.com/paper/2401.16594/) (2024)
- [FedFACT: A Provable Framework for Controllable Group-Fairness Calibration in Federated Learning](https://mlsanity.com/paper/2506.03777/) (2025)

## Abstract (arXiv)

We propose a framework for constructing and analyzing multiclass and multioutput classification metrics, i.e., involving multiple, possibly correlated multiclass labels. Our analysis reveals novel insights on the geometry of feasible confusion tensors -- including necessary and sufficient conditions for the equivalence between optimizing an arbitrary non-decomposable metric and learning a weighted classifier. Further, we analyze averaging methodologies commonly used to compute multioutput metrics and characterize the corresponding Bayes optimal classifiers. We show that the plug-in estimator based on this characterization is consistent and is easily implemented as a post-processing rule. Empirical results on synthetic and benchmark datasets support the theoretical findings.