Optimizing Ensemble Weights and Hyperparameters of Machine Learning Models for Regression Problems

Aggregating multiple learners through an ensemble of models aim to make better predictions by capturing the underlying distribution of the data more accurately. Different ensembling methods, such as bagging, boosting, and stacking/blending, have been studied and adopted extensively in research and practice. While bagging and boosting focus more on reducing variance and bias, respectively, stacking approaches target both by finding the optimal way to combine base learners. In stacking with the weighted average, ensembles are created from weighted averages of multiple base learners. It is known that tuning hyperparameters of each base learner inside the ensemble weight optimization process can produce better performing ensembles. To this end, an optimization-based nested algorithm that considers tuning hyperparameters as well as finding the optimal weights to combine ensembles (Generalized Weighted Ensemble with Internally Tuned Hyperparameters (GEM-ITH)) is designed. Besides, Bayesian search was used to speed-up the optimizing process, and a heuristic was implemented to generate diverse and well-performing base learners. The algorithm is shown to be generalizable to real data sets through analyses with ten publicly available data sets.