Trimmed Maximum Likelihood Estimation for Robust Generalized Linear Model

We study the problem of learning generalized linear models under adversarial corruptions. We analyze a classical heuristic called the \textit{iterative trimmed maximum likelihood estimator} which is known to be effective against \textit{label corruptions} in practice. Under label corruptions, we prove that this simple estimator achieves minimax near-optimal risk on a wide range of generalized linear models, including Gaussian regression, Poisson regression and Binomial regression. Finally, we extend the estimator to the much more challenging setting of \textit{label and covariate corruptions} and demonstrate its robustness and optimality in that setting as well.

Authors

• Pranjal Awasthi
• Abhimanyu Das
• Weihao Kong Shanghai Jiao Tong University
• Rajat Sen

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