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m Mgfbinae moved page Proximal gradient to Proximal gradient methods for learning: Current title does not reflect full content of article, which is proximal gradient methods specifically from a statistical learning theory perspective |
→Exploiting Group Structure: lower case obviously required by WP:MOS |
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where <math>x_i\in \mathbb{R}^d\text{ and } y_i\in\mathbb{R}.</math>
For <math>0<\mu\leq 1</math> the penalty term <math>\lambda \left((1-\mu)\|w\|_1+\mu \|w\|_2\right)</math> is now strictly convex, and hence the minimization problem now admits a unique solution. It has been observed that for sufficiently small <math>\mu > 0</math>, the additional penalty term <math>\mu \|w\|_2</math> acts as a preconditioner and can substantially improve convergence while not adversely affecting the sparsity of solutions.<ref name=structSparse /><ref name=deMolElasticNet>{{cite journal|last=De Mol|first=C.|coauthors=De Vito, E., and Rosasco, L.|title=Elastic-net regularization in learning theory|journal=J. Complexity|year=2009|volume=25|issue=2|pages=201-230|doi=10.1016/j.jco.2009.01.002}}</ref>
== Exploiting
Proximal gradient methods provide a general framework which is applicable to a wide variety of problems in [[statistical learning theory]]. Certain problems in learning can often involve data which has additional structure that is known '' a priori''. In the past several years there have been new developments which incorporate information about group structure to provide methods which are tailored to different applications. Here we survey a few such methods.
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