# Maximum Regularized Likelihood Estimators: A General Prediction Theory and Applications

arXiv: https://arxiv.org/abs/1710.02950 · HTML: https://mlsanity.com/paper/1710.02950/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2017.

## Built on by (most cited first, 1 of 1)

- [Statistical guarantees for sparse deep learning](https://mlsanity.com/paper/2212.05427/) (2022)

## Abstract (arXiv)

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.