ﻻ يوجد ملخص باللغة العربية
We consider the class of convex minimization problems, composed of a self-concordant function, such as the $logdet$ metric, a convex data fidelity term $h(cdot)$ and, a regularizing -- possibly non-smooth -- function $g(cdot)$. This type of problems have recently attracted a great deal of interest, mainly due to their omnipresence in top-notch applications. Under this emph{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.
In this paper, we consider the Graphical Lasso (GL), a popular optimization problem for learning the sparse representations of high-dimensional datasets, which is well-known to be computationally expensive for large-scale problems. Recently, we have
The sparse inverse covariance estimation problem is commonly solved using an $ell_{1}$-regularized Gaussian maximum likelihood estimator known as graphical lasso, but its computational cost becomes prohibitive for large data sets. A recent line of re
Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for each gree
Across a variety of scientific disciplines, sparse inverse covariance estimation is a popular tool for capturing the underlying dependency relationships in multivariate data. Unfortunately, most estimators are not scalable enough to handle the sizes
In sparse principal component analysis we are given noisy observations of a low-rank matrix of dimension $ntimes p$ and seek to reconstruct it under additional sparsity assumptions. In particular, we assume here each of the principal components $math