19,639 research outputs found
Tree-guided group lasso for multi-response regression with structured sparsity, with an application to eQTL mapping
We consider the problem of estimating a sparse multi-response regression
function, with an application to expression quantitative trait locus (eQTL)
mapping, where the goal is to discover genetic variations that influence
gene-expression levels. In particular, we investigate a shrinkage technique
capable of capturing a given hierarchical structure over the responses, such as
a hierarchical clustering tree with leaf nodes for responses and internal nodes
for clusters of related responses at multiple granularity, and we seek to
leverage this structure to recover covariates relevant to each
hierarchically-defined cluster of responses. We propose a tree-guided group
lasso, or tree lasso, for estimating such structured sparsity under
multi-response regression by employing a novel penalty function constructed
from the tree. We describe a systematic weighting scheme for the overlapping
groups in the tree-penalty such that each regression coefficient is penalized
in a balanced manner despite the inhomogeneous multiplicity of group
memberships of the regression coefficients due to overlaps among groups. For
efficient optimization, we employ a smoothing proximal gradient method that was
originally developed for a general class of structured-sparsity-inducing
penalties. Using simulated and yeast data sets, we demonstrate that our method
shows a superior performance in terms of both prediction errors and recovery of
true sparsity patterns, compared to other methods for learning a
multivariate-response regression.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS549 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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
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