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- Jelle J. Goeman, Sara A. van de Geer, Floor de Kort, Hans C. van Houwelingen
- Bioinformatics
- 2004

MOTIVATION
This paper presents a global test to be used for the analysis of microarray data. Using this test it can be determined whether the global expression pattern of a group of genes is significantly related to some clinical outcome of interest. Groups of genes may be any size from a single gene to all genes on the chip (e.g. known pathways, specific… (More)

The group lasso is an extension of the lasso to do variable selection on (predefined) groups of variables in linear regression models. The estimates have the attractive property of being invariant under groupwise orthogonal reparameterizations. We extend the group lasso to logistic regression models and present an efficient algorithm, that is especially… (More)

- Alexandre Tsybakov, Marten Wegkamp, +16 authors Ann Lee
- 2010

Sparse low-dimensional matrix factorization methods applied to biological data with latent structure Graphical model selection in high dimensional settings: Practical methods and fundamental limits

We study the problem of estimating multiple linear regression equations for the purpose of both prediction and variable selection. Following recent work on multi-task learning Argyriou et al. [2008], we assume that the regression vectors share the same sparsity pattern. This means that the set of relevant predictor variables is the same across the different… (More)

We revisit the adaptive Lasso as well as the thresholded Lasso with refitting, in a high-dimensional linear model, and study prediction error, ℓq-error (q ∈ {1, 2}), and number of false positive selections. Our theoretical results for the two methods are, at a rather fine scale, comparable. The differences only show up in terms of the (minimal) restricted… (More)

We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a com-putationally efficient algorithm, with provable numerical convergence properties, for optimizing the penalized likelihood.… (More)

We show that the two-stage adaptive Lasso procedure (Zou, 2006) is consistent for high-dimensional model selection in linear and Gaussian graphical models. Our conditions for consistency cover more general situations than those accomplished in previous work: we prove that restricted eigenvalue conditions (Bickel et al., 2008) are also sufficient for sparse… (More)

We propose an 1-penalized estimation procedure for high-dimensional linear mixed-effects models. The models are useful whenever there is a grouping structure among high-dimensional observations, that is, for clustered data. We prove a consistency and an oracle optimality result and we develop an algorithm with provable numerical convergence. Furthermore, we… (More)

Second Edition This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The… (More)

We consider a linear regression problem in a high dimensional setting where the number of covariates p can be much larger than the sample size n. In such a situation, one often assumes sparsity of the regression vector, i.e., the regression vector contains many zero components. We propose a Lasso-type estimatorˆβ Quad (where 'Quad' stands for quadratic)… (More)