Maximum Regularized Likelihood Estimators: A General Prediction Theory and Applications

Rui Zhuang; Johannes Lederer

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arXiv · 1710.02950

Maximum Regularized Likelihood Estimators: A General Prediction Theory and Applications

Rui Zhuang·Johannes Lederer

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Abstract

Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, 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.

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Rui Zhuang, Johannes Lederer. 2018-10-17. Maximum Regularized Likelihood Estimators: A General Prediction Theory and Applications. https://arxiv.org/abs/1710.02950

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