On Lp-norm Robustness of Ensemble Decision Stumps and Trees

Jul 12, 2020

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Recent papers have demonstrated that ensemble stumps and trees could be vulnerable to small input perturbations, so robustness verification and defense for those models have become an important research problem. However, due to the structure of decision trees, where each node makes decision purely based on one feature value, all the previous works only consider the ℓ_∞ norm perturbation. To study robustness with respect to a general ℓ_p norm perturbation, one has to consider correlation between perturbations on different features, which has not been handled by previous algorithms. In this paper, we study the robustness verification and defense with respect to general ℓ_p norm perturbation for ensemble trees and stumps. For robustness verification, we prove that exact verification is NP-complete for p∈(0, ∞) while polynomial time algorithms exist for p=0 or ∞. Approximation algorithms based on dynamic programming is then developed for verifying ensemble trees and stumps. For robustness training, we propose the first certified defense method for training ensemble stumps and trees with respect to ℓ_p norm perturbations. The effectiveness of proposed algorithms is verified empirically on real datasets.

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The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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