Optimally Weighted Ensembles of Regression Models: Exact Weight Optimization and Applications

TL;DR

This paper introduces an exact and efficient convex quadratic programming approach for optimally weighting ensembles of regression models, outperforming single-model selection on various datasets, including drug discovery data.

Contribution

It develops a novel, exact convex quadratic programming method for optimally combining heterogeneous regression models, improving over heuristic approaches.

Findings

Outperforms model selection methods on multiple datasets

Proves convexity of the quadratic programming formulation

Provides open-source implementation accessible on standard hardware

Abstract

Automated model selection is often proposed to users to choose which machine learning model (or method) to apply to a given regression task. In this paper, we show that combining different regression models can yield better results than selecting a single ('best') regression model, and outline an efficient method that obtains optimally weighted convex linear combination from a heterogeneous set of regression models. More specifically, in this paper, a heuristic weight optimization, used in a preceding conference paper, is replaced by an exact optimization algorithm using convex quadratic programming. We prove convexity of the quadratic programming formulation for the straightforward formulation and for a formulation with weighted data points. The novel weight optimization is not only (more) exact but also more efficient. The methods we develop in this paper are implemented and made available via github-open source. They can be executed on commonly available hardware and offer a transparent and easy to interpret interface. The results indicate that the approach outperforms model selection methods on a range of data sets, including data sets with mixed variable type from drug discovery applications.