Constructing Multiclass Classifiers using Binary Classifiers Under Log-Loss

The construction of multiclass classifiers from binary classifiers is studied in this paper, and performance is quantified by the regret, defined with respect to the Bayes optimal log-loss. We start by proving that the regret of the well known One vs. All (OVA) method is upper bounded by the sum of the regrets of its constituent binary classifiers. We then present a new method called Conditional OVA (COVA), and prove that its regret is given by the weighted sum of the regrets corresponding to the constituent binary classifiers. Lastly, we present a method termed Leveraged COVA (LCOVA), designated to reduce the regret of a multiclass classifier by breaking it down to independently optimized binary classifiers.