A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively applies binary splits to divide the set of classes into two subsets, and trains a binary classifier for each split. Many methods have been proposed to perform this split, each with various advantages and disadvantages. In this paper, we present a simple, general method for improving the predictive performance of nested dichotomies produced by any subset selection techniques that employ randomness to construct the subsets. We provide a theoretical expectation for performance improvements, as well as empirical results showing that our method improves the root mean squared error of nested dichotomies, regardless of whether they are employed as an individual model or in an ensemble setting.

Nested dichotomies are used as a method of transforming a multiclass classification problem into a series of binary problems. A tree structure is induced that recursively splits the set of classes into subsets, and a binary classification model learns to discriminate between the two subsets of classes at each node. In this paper, we demonstrate that these nested dichotomies typically exhibit poor probability calibration, even when the base binary models are well calibrated. We also show that this problem is exacerbated when the binary models are poorly calibrated. We discuss the effectiveness of different calibration strategies and show that accuracy and log-loss can be significantly improved by calibrating both the internal base models and the full nested dichotomy structure, especially when the number of classes is high.

A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively applies binary splits to divide the set of classes into two subsets, and trains a binary classifier for each split. Although ensembles of nested dichotomies with random structure have been shown to perform well in practice, using a more sophisticated class subset selection method can be used to improve classification accuracy. We investigate an approach to this problem called random-pair selection, and evaluate its effectiveness compared to other published methods of subset selection. We show that our method outperforms other methods in many cases when forming ensembles of nested dichotomies, and is at least on par in all other cases.