Speaker: Rui Zhuang, Graduate Student, UW Biostatistics
Abstract: Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this project, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of prediction accuracy. We assume only that the densities have a convex parametrization and that the regularization is definite and positive homogenous. The results thus apply to a very large variety of models and estimators, such as tensor regression and graphical models with convex and non-convex regularized methods. A main conclusion is that MRLEs are broadly consistent in prediction — regardless of whether restricted eigenvalues or similar conditions hold.