Proximal gradient methods for learning: Difference between revisions

Revision as of 16:14, 9 December 2013

Revision as of 16:40, 10 December 2013

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{{user sandbox}}

'''Proximal gradient''' (also known as forward backward splitting) '''methods for learning''' is an area of research in [[optimization]] and [[statistical learning theory]] which studies algorithms for a general class of [[Convex_function#Definition|convex]] [[Regularization_(mathematics)|regularization]] problems where the regularization penalty may not be [[Convex_function#DefinitionDifferentiable_function|strictly convexdifferentiable]]. One such example is <math>\ell_1</math> regularization (also known as Lasso) of the form

:<math>\min_{w\in\mathbb{R}^d} \frac{1}{n}\sum_{i=1}^n (y_i- \langle w,x_i\rangle)^2+ \lambda \|w\|_1, \quad \text{ where } x_i\in \mathbb{R}^d\text{ and } y_i\in\mathbb{R}.</math>