Efficient Monte Carlo Optimization for Multi-dimensional Classifier Chains

Multi-dimensional classification (MDC) is the supervised learning problem where an instance may be associated with multiple classes, rather than with a single class as in traditional binary or multi-class single-dimensional classification (SDC) problems. MDC is closely related to multi-task learning, and multi-target learning (generally, in the literature, multi-target refers to the regression case). Modeling dependencies between labels 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. On the one hand, the original CC algorithm makes a greedy approximation, and is fast but tends to propagate errors down the chain. On the other hand, a recent Bayes-optimal method improves the performance, but is computationally intractable in practice. Here we present novel Monte Carlo schemes, both for finding a good chain sequence and performing efficient inference. Our algorithms remain tractable for high-dimensional data sets and obtains the best overall accuracy, as shown on several real data sets.