Neural Network Ensembles: Theory, Training, and the Importance of Explicit Diversity

Ensemble learning is a process by which multiple base learners are strategically generated and combined into one composite learner. There are two features that are essential to an ensemble's performance, the individual accuracies of the component learners and the overall diversity in the ensemble. The right balance of learner accuracy and ensemble diversity can improve the performance of machine learning tasks on benchmark and real-world data sets, and recent theoretical and practical work has demonstrated the subtle trade-off between accuracy and diversity in an ensemble. In this paper, we extend the extant literature by providing a deeper theoretical understanding for assessing and improving the optimality of any given ensemble, including random forests and deep neural network ensembles. We also propose a training algorithm for neural network ensembles and demonstrate that our approach provides improved performance when compared to both state-of-the-art individual learners and ensembles of state-of-the-art learners trained using standard loss functions. Our key insight is that it is better to explicitly encourage diversity in an ensemble, rather than merely allowing diversity to occur by happenstance, and that rigorous theoretical bounds on the trade-off between diversity and learner accuracy allow one to know when an optimal arrangement has been achieved.