Regularizers for Structured Sparsity

Details Regularizers for Structured Sparsity Regularizers for Structured Sparsity

2010-10-04

arxiv.org/abs/1010.0556v2

Statistics

Machine Learning

Scientific paper

We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. This problem is relevant in machine learning, statistics and signal processing. It is well known that a linear regression can benefit from knowledge that the underlying regression vector is sparse. The combinatorial problem of selecting the nonzero components of this vector can be "relaxed" by regularizing the squared error with a convex penalty function like the $\ell_1$ norm. However, in many applications, additional conditions on the structure of the regression vector and its sparsity pattern are available. Incorporating this information into the learning method may lead to a significant decrease of the estimation error. In this paper, we present a family of convex penalty functions, which encode prior knowledge on the structure of the vector formed by the absolute values of the regression coefficients. This family subsumes the $\ell_1$ norm and is flexible enough to include different models of sparsity patterns, which are of practical and theoretical importance. We establish the basic properties of these penalty functions and discuss some examples where they can be computed explicitly. Moreover, we present a convergent optimization algorithm for solving regularized least squares with these penalty functions. Numerical simulations highlight the benefit of structured sparsity and the advantage offered by our approach over the Lasso method and other related methods.

Affiliated with

Also associated with

No associations

Rating

Regularizers for Structured Sparsity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Regularizers for Structured Sparsity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regularizers for Structured Sparsity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-274539