Formal Verification and Summarization of Results for Tree Ensemble Models

Abstract

Since the inference of machine learning models is inductive and generally a complex black box, it is difficult to apply conventional software testing methods, but formal testing methods for machine learning software are needed to guarantee the quality. We propose a formal verification method for decision-tree-based ensemble models that can rigorously verify whether a model satisfies the expected verification properties and summarize the verification results. The proposed method exhaustively enumerates verification violations by efficiently searching the input space of verification properties, and summarizes the violation regions such that the discovered violations can be properly addressed. Experimental results on four datasets for three tasks (regression, binary classification, and multiclass classification) confirm that the proposed method can complete the verification more efficiently than existing methods. Furthermore, a comparison of evaluation metrics to quantify the quality of the summarized violation regions shows that the proposed method can achieve higher quality than existing methods.