# Constructing Multiclass Classifiers using Binary Classifiers Under Log-Loss

arXiv: https://arxiv.org/abs/2102.08184 · HTML: https://mlsanity.com/paper/2102.08184/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 29 references that are in the map.
- First posted on arXiv 16 Feb 2021.

## Builds on (most cited first, 2 of 2)

- [Minimum Excess Risk in Bayesian Learning](https://mlsanity.com/paper/2012.14868/) (2020)
- [Pitfalls of Assessing Extracted Hierarchies for Multi-Class Classification](https://mlsanity.com/paper/2101.11095/) (2021)

## Built on by (most cited first, 1 of 1)

- [Machine learning approach to detect dynamical states from recurrence measures](https://mlsanity.com/paper/2401.10298/) (2024)

## Abstract (arXiv)

The construction of multiclass classifiers from binary elements is studied in this paper, and performance is quantified by the regret, defined with respect to the Bayes optimal log-loss. We discuss two known methods. The first is one vs. all (OVA), for which we prove that the multiclass regret is upper bounded by the sum of binary regrets of the constituent classifiers. The second is hierarchical classification, based on a binary tree. For this method we prove that the multiclass regret is exactly a weighted sum of constituent binary regrets where the weighing is determined by the tree structure. We also introduce a leverage-hierarchical classification method, which potentially yields smaller log-loss and regret. The advantages of these classification methods are demonstrated by simulation on both synthetic and real-life datasets.