Trimmed Maximum Likelihood Estimation for Robust Learning in Generalized Linear Models

Understand

We study the problem of learning generalized linear models under adversarial corruptions.

• We analyze a classical heuristic called the iterative trimmed maximum likelihood estimator which is known to be effective against 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 more challenging setting of label and covariate corruptions and demonstrate its robustness and optimality in that setting as well.