2,142 research outputs found
Optimization with Sparsity-Inducing Penalties
Sparse estimation methods are aimed at using or obtaining parsimonious
representations of data or models. They were first dedicated to linear variable
selection but numerous extensions have now emerged such as structured sparsity
or kernel selection. It turns out that many of the related estimation problems
can be cast as convex optimization problems by regularizing the empirical risk
with appropriate non-smooth norms. The goal of this paper is to present from a
general perspective optimization tools and techniques dedicated to such
sparsity-inducing penalties. We cover proximal methods, block-coordinate
descent, reweighted -penalized techniques, working-set and homotopy
methods, as well as non-convex formulations and extensions, and provide an
extensive set of experiments to compare various algorithms from a computational
point of view
Smoothing Proximal Gradient Method for General Structured Sparse Learning
We study the problem of learning high dimensional regression models
regularized by a structured-sparsity-inducing penalty that encodes prior
structural information on either input or output sides. We consider two widely
adopted types of such penalties as our motivating examples: 1) overlapping
group lasso penalty, based on the l1/l2 mixed-norm penalty, and 2) graph-guided
fusion penalty. For both types of penalties, due to their non-separability,
developing an efficient optimization method has remained a challenging problem.
In this paper, we propose a general optimization approach, called smoothing
proximal gradient method, which can solve the structured sparse regression
problems with a smooth convex loss and a wide spectrum of
structured-sparsity-inducing penalties. Our approach is based on a general
smoothing technique of Nesterov. It achieves a convergence rate faster than the
standard first-order method, subgradient method, and is much more scalable than
the most widely used interior-point method. Numerical results are reported to
demonstrate the efficiency and scalability of the proposed method.Comment: arXiv admin note: substantial text overlap with arXiv:1005.471
Pathway-Based Genomics Prediction using Generalized Elastic Net.
We present a novel regularization scheme called The Generalized Elastic Net (GELnet) that incorporates gene pathway information into feature selection. The proposed formulation is applicable to a wide variety of problems in which the interpretation of predictive features using known molecular interactions is desired. The method naturally steers solutions toward sets of mechanistically interlinked genes. Using experiments on synthetic data, we demonstrate that pathway-guided results maintain, and often improve, the accuracy of predictors even in cases where the full gene network is unknown. We apply the method to predict the drug response of breast cancer cell lines. GELnet is able to reveal genetic determinants of sensitivity and resistance for several compounds. In particular, for an EGFR/HER2 inhibitor, it finds a possible trans-differentiation resistance mechanism missed by the corresponding pathway agnostic approach
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