Trimmed Maximum Likelihood Estimation for Robust Learning in Generalized Linear Models
This work addresses robust statistical learning for generalized linear models, providing theoretical guarantees against adversarial corruptions, but it is incremental as it builds on a classical heuristic.
The paper tackles robust learning in generalized linear models under adversarial corruptions by analyzing the iterative trimmed maximum likelihood estimator, proving it achieves minimax near-optimal risk for label corruptions across models like Gaussian, Poisson, and Binomial regression, and extends it to handle label and covariate corruptions with demonstrated robustness and optimality.
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.