A study of error variance estimation in Lasso regression

Reid, Stephen; Tibshirani, Robert; Friedman, Jerome H.

doi:10.5705/ss.2014.042

Cited by 124 publications

(135 citation statements)

References 11 publications

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“…Estimation of the error variance in high‐dimensional (

p > n

) settings is an active research area. For an overview of some possible methods to estimate the error variance see, for example, Reid et al (). For simplicity, we provide the covariance test with the true error variance in order to assess its performance independently of any variance estimation procedure .…”

Section: Simulationsmentioning

confidence: 99%

A Permutation Approach for Selecting the Penalty Parameter in Penalized Model Selection

2015

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Summary We describe a simple, computationally effcient, permutation-based procedure for selecting the penalty parameter in LASSO penalized regression. The procedure, permutation selection, is intended for applications where variable selection is the primary focus, and can be applied in a variety of structural settings, including that of generalized linear models. We briefly discuss connections between permutation selection and existing theory for the LASSO. In addition, we present a simulation study and an analysis of real biomedical data sets in which permutation selection is compared with selection based on the following: cross-validation (CV), the Bayesian information criterion (BIC), Scaled Sparse Linear Regression, and a selection method based on recently developed testing procedures for the LASSO.

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“…Estimation of the error variance in high‐dimensional (

p > n

Section: Simulationsmentioning

confidence: 99%

A Permutation Approach for Selecting the Penalty Parameter in Penalized Model Selection

2015

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“…We also evaluated the overall PVE explained by all the SNPs which approximates the narrow sense heritability of the trait on the basis of the LASSO estimates following Sillanpää ():

{PVE}_{normaltotal} = \frac{var (\sum_{j = 1}^{p} {boldx}_{j} {\overset{β}{true}}_{j})}{var (y)} \approx \frac{var false(boldy false) - {\overset{σ}{true}}_{0}^{2}}{var (y)},

where

{\overset{false^}{normalσ}}_{0}^{2}

is the LASSO residual variance estimated by a cross‐validation‐based estimator introduced by Reid et al . ().…”

Section: Methodsmentioning

confidence: 97%

“…wherer 2 0 is the LASSO residual variance estimated by a cross-validation-based estimator introduced by Reid et al (2016).…”

Section: Qtl Mappingmentioning

confidence: 99%

Deciphering the genomic architecture of the stickleback brain with a novel multilocus gene‐mapping approach

Guo

Yang

et al. 2017

Molecular Ecology

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Quantitative traits important to organismal function and fitness, such as brain size, are presumably controlled by many small-effect loci. Deciphering the genetic architecture of such traits with traditional quantitative trait locus (QTL) mapping methods is challenging. Here, we investigated the genetic architecture of brain size (and the size of five different brain parts) in nine-spined sticklebacks (Pungitius pungitius) with the aid of novel multilocus QTL-mapping approaches based on a de-biased LASSO method. Apart from having more statistical power to detect QTL and reduced rate of false positives than conventional QTL-mapping approaches, the developed methods can handle large marker panels and provide estimates of genomic heritability. Single-locus analyses of an F interpopulation cross with 239 individuals and 15 198, fully informative single nucleotide polymorphisms (SNPs) uncovered 79 QTL associated with variation in stickleback brain size traits. Many of these loci were in strong linkage disequilibrium (LD) with each other, and consequently, a multilocus mapping of individual SNPs, accounting for LD structure in the data, recovered only four significant QTL. However, a multilocus mapping of SNPs grouped by linkage group (LG) identified 14 LGs (1-6 depending on the trait) that influence variation in brain traits. For instance, 17.6% of the variation in relative brain size was explainable by cumulative effects of SNPs distributed over six LGs, whereas 42% of the variation was accounted for by all 21 LGs. Hence, the results suggest that variation in stickleback brain traits is influenced by many small-effect loci. Apart from suggesting moderately heritable (h ≈ 0.15-0.42) multifactorial genetic architecture of brain traits, the results highlight the challenges in identifying the loci contributing to variation in quantitative traits. Nevertheless, the results demonstrate that the novel QTL-mapping approach developed here has distinctive advantages over the traditional QTL-mapping methods in analyses of dense marker panels.

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“…In our study, we examine the performance of BVS CLR relative to that of lasso CLR with respect to selection and prediction accuracy. Although variance estimation approaches for lasso regression exist [40, 41], we take a more straightforward approach and consider, for both BVS and lasso CLR, a rough MSE approximation using the empirical mean of the squared deviations between the estimated and actual β k values. We run all analyses using R software version 3.1.2 [42].…”

Section: Simulation Studiesmentioning

confidence: 99%

Bayesian Variable Selection Methods for Matched Case-Control Studies

Asafu‐Adjei

Mahlet

Coull

et al. 2017

The International Journal of Biostatistics

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Matched case-control designs are currently used in many biomedical applications. To ensure high efficiency and statistical power in identifying features that best discriminate cases from controls, it is important to account for the use of matched designs. However, in the setting of high dimensional data, few variable selection methods account for matching. Bayesian approaches to variable selection have several advantages, including the fact that such approaches visit a wider range of model subsets. In this paper, we propose a variable selection method to account for case-control matching in a Bayesian context and apply it using simulation studies, a matched brain imaging study conducted at Massachusetts General Hospital, and a matched cardiovascular biomarker study conducted by the High Risk Plaque Initiative.

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A study of error variance estimation in Lasso regression

Cited by 124 publications

References 11 publications

A Permutation Approach for Selecting the Penalty Parameter in Penalized Model Selection

A Permutation Approach for Selecting the Penalty Parameter in Penalized Model Selection

Deciphering the genomic architecture of the stickleback brain with a novel multilocus gene‐mapping approach

Bayesian Variable Selection Methods for Matched Case-Control Studies

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