Efficient Monte Carlo Methods for Multi-Dimensional Learning with Classifier Chains

Multidimensional classification (MDC) is the supervised learning problem where an instance is associated with multiple classes, rather than with a single class, as in traditional classification problems. Since these classes are often strongly correlated, modeling the dependencies between them allows MDC methods to improve their performance - at the expense of an increased computational cost. In this paper we focus on the classifier chains (CC) approach for modeling dependencies, one of the most popular and highestperforming methods for multi-label classification (MLC), a particular case of MDC which involves only binary classes (i.e., labels). The original CC algorithm makes a greedy approximation, and is fast but tends to propagate errors along the chain. Our algorithms remain tractable for high-dimensional data sets and obtain the best predictive performance across several real data sets. Keywords: classifier chains, multidimensional classification, multi-label classification, Monte Carlo methods, Bayesian inference 1. Introduction Multidimensional classification (MDC) is the supervised learning problem where an instance may be associated with multiple classes, rather than Preprint submitted to Pattern Recognition March 22, 2018 with a single class as in traditional binary or multi-class single-dimensional classification (SDC) problems. So-called MDC (e.g., in [1]) is also known in the literature as multi-target, multi-output [2], or multi-objective [3] classification The recently popularised task of multi-label classification (see [4, 5, 6, 7] for overviews) can be viewed as a particular case of the multidimensional problem that only involves binary classes, i.e., labels that can be turned on (1) or off (0) for any data instance. The MDC learning context is receiving increased attention in the literature, since it arises naturally in a wide variety of domains, such as image classification [8, 9], information retrieval and text categorization [10], automated detection of emotions in music [11] or bioinformatics [10, 12].