Robust Volume Ratio: A Metric for Fine-Grained Evaluation of Tree Ensemble Robustness

Ensuring the reliability of systems that incorporate machine learning models requires rigorous verification and risk management. This paper introduces a novel metric and methodology for evaluating the robustness of tree ensemble models. While conventional metrics, such as maximum safe radius and adversarial accuracy, remain valuable, they often fail to capture the full scope of robustness. In particular, they tend to overlook the proportion and extent of safe versus unsafe regions surrounding individual data points, and they rarely characterize the full set of possible adversarial examples. To address these limitations, we propose the robust volume ratio (RVR), a new metric that quantifies the robustness of individual data samples against adversarial perturbations by measuring the volume of robust regions in the local input space. By efficiently enumerating both robust and non-robust regions through the structure of the model, we enable precise computations of both the RVR and the exact maximum safe radius. Experimental results demonstrate that these comprehensive metrics can be computed efficiently and support a multifaceted, fine-grained evaluation of model robustness.