Trimmed Maximum Likelihood Estimation for Robust Generalized Linear Model
Pranjal Awasthi,Abhimanyu Das,Weihao Kong,Rajat Sen
We study the problem of learning generalized linear models under adversarial corruptions.We analyze a classical heuristic called the extit{iterative trimmed maximum likelihood estimator} which is known to be effective against extit{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 extit{label and covariate corruptions} and demonstrate its robustness and optimality in that setting as well.
