Robust Logistic Regression and Classification

Part of Advances in Neural Information Processing Systems 27 (NIPS 2014)

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Jiashi Feng, Huan Xu, Shie Mannor, Shuicheng Yan


We consider logistic regression with arbitrary outliers in the covariate matrix. We propose a new robust logistic regression algorithm, called RoLR, that estimates the parameter through a simple linear programming procedure. We prove that RoLR is robust to a constant fraction of adversarial outliers. To the best of our knowledge, this is the first result on estimating logistic regression model when the covariate matrix is corrupted with any performance guarantees. Besides regression, we apply RoLR to solving binary classification problems where a fraction of training samples are corrupted.