Constructing Multiclass Classifiers using Binary Classifiers Under Log-Loss
This work addresses multiclass classification efficiency for machine learning practitioners, but it is incremental as it builds on known methods with new theoretical bounds and a minor variant.
The paper tackles the problem of constructing multiclass classifiers from binary classifiers by analyzing regret under log-loss, proving bounds for one-vs-all and hierarchical methods and introducing a leverage-hierarchical method that reduces regret, with advantages demonstrated through simulations on synthetic and real datasets.
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.