Scalable Sparse Covariance Estimation via Self-Concordance
Abstract
We consider the class of convex minimization problems, composed of a self-concordant function, such as the logdet metric, a convex data fidelity term h(.) and, a regularizing — possibly non-smooth — function g(.). This type of problems have recently attracted a great deal of interest, mainly due to their omnipresence in top-notch applications. Under this locally Lipschitz continuous gradient setting, we analyze the convergence behavior of proximal Newton schemes with the added twist of a probable presence of inexact evaluations. We prove attractive convergence rate guarantees and enhance state-of-the-art optimization schemes to accommodate such developments. Experimental results on sparse covariance estimation show the merits of our algorithm, both in terms of recovery efficiency and complexity.
Cite
Text
Kyrillidis et al. "Scalable Sparse Covariance Estimation via Self-Concordance." AAAI Conference on Artificial Intelligence, 2014. doi:10.1609/AAAI.V28I1.8960Markdown
[Kyrillidis et al. "Scalable Sparse Covariance Estimation via Self-Concordance." AAAI Conference on Artificial Intelligence, 2014.](https://mlanthology.org/aaai/2014/kyrillidis2014aaai-scalable/) doi:10.1609/AAAI.V28I1.8960BibTeX
@inproceedings{kyrillidis2014aaai-scalable,
title = {{Scalable Sparse Covariance Estimation via Self-Concordance}},
author = {Kyrillidis, Anastasios and Mahabadi, Rabeeh Karimi and Tran-Dinh, Quoc and Cevher, Volkan},
booktitle = {AAAI Conference on Artificial Intelligence},
year = {2014},
pages = {1946-1952},
doi = {10.1609/AAAI.V28I1.8960},
url = {https://mlanthology.org/aaai/2014/kyrillidis2014aaai-scalable/}
}