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Elastic Net (elastic + net)
Selected AbstractsMultistage analysis strategies for genome-wide association studies: summary of group 3 contributions to Genetic Analysis Workshop 16GENETIC EPIDEMIOLOGY, Issue S1 2009Rosalind J. Neuman Abstract This contribution summarizes the work done by six independent teams of investigators to identify the genetic and non-genetic variants that work together or independently to predispose to disease. The theme addressed in these studies is multistage strategies in the context of genome-wide association studies (GWAS). The work performed comes from Group 3 of the Genetic Analysis Workshop 16 held in St. Louis, Missouri in September 2008. These six studies represent a diversity of multistage methods of which five are applied to the North American Rheumatoid Arthritis Consortium rheumatoid arthritis case-control data, and one method is applied to the low-density lipoprotein phenotype in the Framingham Heart Study simulated data. In the first stage of analyses, the majority of studies used a variety of screening techniques to reduce the noise of single-nucleotide polymorphisms purportedly not involved in the phenotype of interest. Three studies analyzed the data using penalized regression models, either LASSO or the elastic net. The main result was a reconfirmation of the involvement of variants in the HLA region on chromosome 6 with rheumatoid arthritis. The hope is that the intense computational methods highlighted in this group of papers will become useful tools in future GWAS. Genet. Epidemiol. 33 (Suppl. 1):S19,S23, 2009. © 2009 Wiley-Liss, Inc. [source] Regression by L1 regularization of smart contrasts and sums (ROSCAS) beats PLS and elastic net in latent variable modelJOURNAL OF CHEMOMETRICS, Issue 5 2009Cajo J. F. ter Braak Abstract This paper proposes a regression method, ROSCAS, which regularizes smart contrasts and sums of regression coefficients by an L1 penalty. The contrasts and sums are based on the sample correlation matrix of the predictors and are suggested by a latent variable regression model. The contrasts express the idea that a priori correlated predictors should have similar coefficients. The method has excellent predictive performance in situations, where there are groups of predictors with each group representing an independent feature that influences the response. In particular, when the groups differ in size, ROSCAS can outperform LASSO, elastic net, partial least squares (PLS) and ridge regression by a factor of two or three in terms of mean squared error. In other simulation setups and on real data, ROSCAS performs competitively. Copyright © 2009 John Wiley & Sons, Ltd. [source] On the non-negative garrotte estimatorJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2007Ming Yuan Summary., We study the non-negative garrotte estimator from three different aspects: consistency, computation and flexibility. We argue that the non-negative garrotte is a general procedure that can be used in combination with estimators other than the original least squares estimator as in its original form. In particular, we consider using the lasso, the elastic net and ridge regression along with ordinary least squares as the initial estimate in the non-negative garrotte. We prove that the non-negative garrotte has the nice property that, with probability tending to 1, the solution path contains an estimate that correctly identifies the set of important variables and is consistent for the coefficients of the important variables, whereas such a property may not be valid for the initial estimators. In general, we show that the non-negative garrotte can turn a consistent estimate into an estimate that is not only consistent in terms of estimation but also in terms of variable selection. We also show that the non-negative garrotte has a piecewise linear solution path. Using this fact, we propose an efficient algorithm for computing the whole solution path for the non-negative garrotte. Simulations and a real example demonstrate that the non-negative garrotte is very effective in improving on the initial estimator in terms of variable selection and estimation accuracy. [source] High-Dimensional Cox Models: The Choice of Penalty as Part of the Model Building ProcessBIOMETRICAL JOURNAL, Issue 1 2010Axel Benner Abstract The Cox proportional hazards regression model is the most popular approach to model covariate information for survival times. In this context, the development of high-dimensional models where the number of covariates is much larger than the number of observations ( ) is an ongoing challenge. A practicable approach is to use ridge penalized Cox regression in such situations. Beside focussing on finding the best prediction rule, one is often interested in determining a subset of covariates that are the most important ones for prognosis. This could be a gene set in the biostatistical analysis of microarray data. Covariate selection can then, for example, be done by L1 -penalized Cox regression using the lasso (Tibshirani (1997). Statistics in Medicine16, 385,395). Several approaches beyond the lasso, that incorporate covariate selection, have been developed in recent years. This includes modifications of the lasso as well as nonconvex variants such as smoothly clipped absolute deviation (SCAD) (Fan and Li (2001). Journal of the American Statistical Association96, 1348,1360; Fan and Li (2002). The Annals of Statistics30, 74,99). The purpose of this article is to implement them practically into the model building process when analyzing high-dimensional data with the Cox proportional hazards model. To evaluate penalized regression models beyond the lasso, we included SCAD variants and the adaptive lasso (Zou (2006). Journal of the American Statistical Association101, 1418,1429). We compare them with "standard" applications such as ridge regression, the lasso, and the elastic net. Predictive accuracy, features of variable selection, and estimation bias will be studied to assess the practical use of these methods. We observed that the performance of SCAD and adaptive lasso is highly dependent on nontrivial preselection procedures. A practical solution to this problem does not yet exist. Since there is high risk of missing relevant covariates when using SCAD or adaptive lasso applied after an inappropriate initial selection step, we recommend to stay with lasso or the elastic net in actual data applications. But with respect to the promising results for truly sparse models, we see some advantage of SCAD and adaptive lasso, if better preselection procedures would be available. This requires further methodological research. [source] Incorporating Predictor Network in Penalized Regression with Application to Microarray DataBIOMETRICS, Issue 2 2010Wei Pan Summary We consider penalized linear regression, especially for "large,p, small,n" problems, for which the relationships among predictors are described a priori by a network. A class of motivating examples includes modeling a phenotype through gene expression profiles while accounting for coordinated functioning of genes in the form of biological pathways or networks. To incorporate the prior knowledge of the similar effect sizes of neighboring predictors in a network, we propose a grouped penalty based on the,L, -norm that smoothes the regression coefficients of the predictors over the network. The main feature of the proposed method is its ability to automatically realize grouped variable selection and exploit grouping effects. We also discuss effects of the choices of the , and some weights inside the,L, -norm. Simulation studies demonstrate the superior finite-sample performance of the proposed method as compared to Lasso, elastic net, and a recently proposed network-based method. The new method performs best in variable selection across all simulation set-ups considered. For illustration, the method is applied to a microarray dataset to predict survival times for some glioblastoma patients using a gene expression dataset and a gene network compiled from some Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways. [source] | ||||||||||