Is Ordered Weighted ${\ell }_1$ Regularized Regression Robust to Adversarial Perturbation? A Case Study on OSCAR

Abstract

Many state-of-the-art machine learning models such as deep neural networks have recently shown to be vulnerable to adversarial perturbations, especially in classification tasks. Motivated by adversarial machine learning, in this paper we investigate the robustness of sparse regression models with strongly correlated covariates to adversarially designed measurement noises. Specifically, we consider the family of ordered weighted ${\ell }_1$ (OWL) regularized regression methods and study the case of OSCAR (octagonal shrinkage clustering algorithm for regression) in the adversarial setting. Under a norm-bounded threat model, we formulate the process of finding a maximally disruptive noise for OWL-regularized regression as an optimization problem and illustrate the steps towards finding such a noise in the case of OSCAR. Experimental results demonstrate that the regression performance of grouping strongly correlated features can be severely degraded under our adversarial setting, even when the noise budget is significantly smaller than the ground-truth signals.

arXiv commentAccepted to IEEE GlobalSIP 2018. Pin-Yu Chen and Bhanukiran Vinzamuri contribute equally to this work; v2 fixes missing citation

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Cited by in corpus (1)

• PROVEN: Certifying Robustness of Neural Networks with a Probabilistic Approach