An Abstraction-Refinement Approach to Formal Verification of Tree Ensembles

Abstract

Recent advances in machine learning are now being considered for integration in safety-critical systems such as vehicles, medical equipment and critical infrastructure. However, organizations in these domains are currently unable to provide convincing arguments that systems integrating machine learning technologies are safe to operate in their intended environments. In this paper, we present a formal verification method for tree ensembles that leverage an abstraction-refinement approach to counteract combinatorial explosion. We implemented the method as an extension to a tool named VoTE, and demonstrate its applicability by verifying the robustness against perturbations in random forests and gradient boosting machines in two case studies. Our abstraction-refinement based extension to VoTE improves the performance by several orders of magnitude, scaling to tree ensembles with up to 50 trees with depth 10, trained on high-dimensional data.