Sciweavers

Share
CORR
2011
Springer

Fast global convergence of gradient methods for high-dimensional statistical recovery

9 years 6 months ago
Fast global convergence of gradient methods for high-dimensional statistical recovery
Many statistical M-estimators are based on convex optimization problems formed by the weighted sum of a loss function with a norm-based regularizer. We analyze the convergence rates of first-order gradient methods for solving such problems within a high-dimensional framework that allows the data dimension d to grow with (and possibly exceed) the sample size n. This high-dimensional structure precludes the usual global assumptions— namely, strong convexity and smoothness conditions—that underlie classical optimization analysis. We define appropriately restricted versions of these conditions, and show that they are satisfied with high probability for various statistical models. Under these conditions, our theory guarantees that Nesterov’s first-order method [12] has a globally geometric rate of convergence up to the statistical precision of the model, meaning the typical Euclidean distance between the true unknown parameter θ∗ and the optimal solution θ. This globally line...
Alekh Agarwal, Sahand Negahban, Martin J. Wainwrig
Added 13 May 2011
Updated 13 May 2011
Type Journal
Year 2011
Where CORR
Authors Alekh Agarwal, Sahand Negahban, Martin J. Wainwright
Comments (0)
books