Provably Robust Random Forests via Certified Perturbation Bounds: A Comprehensive Framework

The widespread adoption of machine learning models in safety-critical and security-sensitive applications has underscored the urgent need for robust and reliable decision-making systems. While many machine learning models, including Random Forests, exhibit excellent performance on clean data, they are highly susceptible to adversarial examples—subtly perturbed inputs crafted to mislead the model into making erroneous predictions. This vulnerability poses a significant threat, undermining trust and limiting the deployment of these powerful tools. This paper addresses the critical challenge of ensuring the robustness of Random Forests by introducing a novel framework for achieving provable guarantees against adversarial perturbations. We propose a methodology that integrates certified perturbation bounds directly into the Random Forest paradigm, enabling the quantification of robustness for individual predictions. Our approach focuses on developing techniques to certify that, within a specified perturbation radius, the model's output remains invariant, providing a strong mathematical guarantee against adversarial attacks. We detail the theoretical underpinnings, including the formulation of certified bounds for individual decision trees and their aggregation within an ensemble, and discuss the practical implications for robust model training and verification. The framework aims to enhance the trustworthiness of Random Forests by moving beyond empirical defenses to provide verifiable assurances of their resilience to adversarial manipulation.