MetaBags: Bagged Meta-Decision Trees for Regression

Abstract

Ensembles are popular methods for solving practical supervised learning problems. They reduce the risk of having underperforming models in production-grade software. Although critical, methods for learning heterogeneous regression ensembles have not been proposed at large scale, whereas in classical ML literature, stacking, cascading and voting are mostly restricted to classification problems. Regression poses distinct learning challenges that may result in poor performance, even when using well established homogeneous ensemble schemas such as bagging or boosting. In this paper, we introduce MetaBags, a novel, practically useful stacking framework for regression. MetaBags is a meta-learning algorithm that learns a set of meta-decision trees designed to select one base model (i.e. expert) for each query, and focuses on inductive bias reduction. A set of meta-decision trees are learned using different types of meta-features, specially created for this purpose - to then be bagged at meta-level. This procedure is designed to learn a model with a fair bias-variance trade-off, and its improvement over base model performance is correlated with the prediction diversity of different experts on specific input space subregions. The proposed method and meta-features are designed in such a way that they enable good predictive performance even in subregions of space which are not adequately represented in the available training data. An exhaustive empirical testing of the method was performed, evaluating both generalization error and scalability of the approach on synthetic, open and real-world application datasets. The obtained results show that our method significantly outperforms existing state-of-the-art approaches.