**No.**
1010

**Title:**

- Learning Binary Classifiers for Multi-Class Problem

**Author(s): **

- Ikeda, Shiro (The Institute of Statistical Mathematics)

**Key words: **

- multi-class classification; Bradley-Terry model; alpha-divergence; maximum likelihood estimation

**Abstract: **

- One important idea for the multi-class classification problem is to combine binary classifiers (base classifiers), which is summarized as error correcting output codes (ECOC), and the generalized Bradley-Terry (GBT) model gives a method to estimate the multi-class probability. In this memo, we review the multi-class problem with the GBT model and discuss two issues. First, a new estimation algorithm of the GBT model associated with $\alpha $--divergence is proposed. Secondly, the maximum likelihood estimation (MLE) algorithm of each base classifier based on the combined multi-class probability is derived.