Oracle inequalities for square root analysis estimators with application to total variation penalties
Statistics Theory
2021-02-12 v2 Machine Learning
Statistics Theory
Abstract
Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan, Hebiri and Lederer (2017). We then extend the theory to the square root analysis estimator. Finally, we focus on (square root) total variation regularized estimators on graphs and obtain constant-friendly rates, which, up to log-terms, match previous results obtained by entropy calculations. We also obtain an oracle inequality for the (square root) total variation regularized estimator over the cycle graph.
Cite
@article{arxiv.1902.11192,
title = {Oracle inequalities for square root analysis estimators with application to total variation penalties},
author = {Francesco Ortelli and Sara van de Geer},
journal= {arXiv preprint arXiv:1902.11192},
year = {2021}
}