Maximum Regularized Likelihood Estimators: A General Prediction Theory and Applications [article]

Rui Zhuang, Johannes Lederer
<span title="2018-10-17">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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
more &raquo; ... dels 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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