Covariate Selection in High-Dimensional Generalized Linear Models With Measurement Error

Errors-in-variables models in high-dimensional settings pose two challenges in application. First, the number of observed covariates is larger than the sample size, while only a small number of covariates are true predictors under an assumption of model sparsity. Second, the presence of measurement error can result in severely biased parameter estimates, and also affects the ability of penalized methods such as the lasso to recover the true sparsity pattern. A new estimation procedure called SIMulation-SELection-EXtrapolation (SIMSELEX) is proposed. This procedure makes double use of lasso methodology. First, the lasso is used to estimate sparse solutions in the simulation step, after which a group lasso is implemented to do variable selection. The SIMSELEX estimator is shown to perform well in variable selection, and has significantly lower estimation error than naive estimators that ignore measurement error. SIMSELEX can be applied in a variety of errors-in-variables settings, including linear models, generalized linear models, and Cox survival models. It is furthermore shown in the Supporting Information how SIMSELEX can be applied to spline-based regression models. A simulation study is conducted to compare the SIMSELEX estimators to existing methods in the linear and logistic model settings, and to evaluate performance compared to naive methods in the Cox and spline models. Finally, the method is used to analyze a microarray dataset that contains gene expression measurements of favorable histology Wilms tumors.

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“…Sørensen et al . () proposed a GMUS for sparse high‐dimensional GLM models with measurement error. The GMUS estimator does not make use of

Σ_{u}

.…”

Section: Model Illustration and Simulation Resultsmentioning

confidence: 99%

“…Additionally, Sørensen et al . () developed the generalized matrix uncertainty selector (GMUS) for generalized linear models. Both the conditional score approach and GMUS require subjective choices of tuning parameters.…”

Section: Introductionmentioning

confidence: 99%

Simulation-Selection-Extrapolation: Estimation in High-Dimensional Errors-in-Variables Models

Nghiem

Potgieter

2019

Biometrics

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“…In future work, we will also extend the estimation methods to the settings where the covariates are measured with multiplicative errors which are shown to be reducible to the additive error problem as studied in the present work [36,30]. Moreover, we are interested in applying the analysis and concentration of measure results developed in the current paper and in our ongoing work to the more general contexts and settings where measurement error models are introduced and investigated; see for example [16,8,44,24,20,45,9,7,14,46,25,28,47,53,23,29,32,2,43,41,42] and references therein.…”

Section: Discussionmentioning

confidence: 98%

Errors-in-variables models with dependent measurements

Rudelson¹,

Zhou²

2017

Electron. J. Statist.

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Suppose that we observe y ∈ R n and X ∈ R n×m in the following errors-invariables model:where X 0 is an n × m design matrix with independent subgaussian row vectors, ∈ R n is a noise vector and W is a mean zero n × m random noise matrix with independent subgaussian column vectors, independent of X 0 and . This model is significantly different from those analyzed in the literature in the sense that we allow the measurement error for each covariate to be a dependent vector across its n observations. Such error structures appear in the science literature when modeling the trial-to-trial fluctuations in response strength shared across a set of neurons.Under sparsity and restrictive eigenvalue type of conditions, we show that one is able to recover a sparse vector β * ∈ R m from the model given a single observation matrix X and the response vector y. We establish consistency in estimating β * and obtain the rates of convergence in the q norm, where q = 1, 2 for the Lasso-type estimator, and for q ∈ [1, 2] for a Dantzig-type Conic programming estimator. We show error bounds which approach that of the regular Lasso and the Dantzig selector in case the errors in W are tending to 0. We analyze the convergence rates of the gradient descent methods for solving the nonconvex programs and show that the composite gradient descent algorithm is guaranteed to converge at a geometric rate to a neighborhood of the global minimizers: the size of the neighborhood is bounded by the statistical error in the 2 norm. Our analysis reveals interesting connections between computational and statistical efficiency and the concentration of measure phenomenon in random matrix theory. We provide simulation evidence illuminating the theoretical predictions.MSC 2010 subject classifications: Primary 60K35, 60K35; secondary 60K35.

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“…We present an architecture that recovers missing expression data for multiple tissue types under the missing completely at random assumption (MCAR; Little and Rubin, 2019), that is, the missingness of the data is independent of the observed and the missing variables. In contrast to existing linear methods for deconfounding gene expression (Øystein Sørensen et al, 2018), our model integrates covariates (global determinants of gene expression; Stegle et al, 2012) to account for their non-linear effects. In particular, a characteristic feature of our architecture is the use of word embeddings (Mikolov et al, 2013) to learn rich and distributed representations for the tissue types and other covariates.…”

Section: Introductionmentioning

confidence: 99%

Gene Expression Imputation with Generative Adversarial Imputation Nets

Torne¹,

Azevedo²,

Gamazon³

et al. 2020

Preprint

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A question of fundamental biological significance is to what extent the expression of a subset of genes can be used to recover the full transcriptome, with important implications for biological discovery and clinical application. To address this challenge, we present GAIN-GTEx, a method for gene expression imputation based on Generative Adversarial Imputation Networks. In order to increase the applicability of our approach, we leverage data from GTEx v8, a reference resource that has generated a comprehensive collection of transcriptomes from a diverse set of human tissues. We compare our model to several standard and state-of-theart imputation methods and show that GAIN-GTEx is significantly superior in terms of predictive performance and runtime. Furthermore, our results indicate strong generalisation on RNA-Seq data from 3 cancer types across varying levels of missingness. Our work can facilitate a cost-effective integration of large-scale RNA biorepositories into genomic studies of disease, with high applicability across diverse tissue types.

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Covariate Selection in High-Dimensional Generalized Linear Models With Measurement Error

Cited by 28 publications

References 36 publications

Simulation-Selection-Extrapolation: Estimation in High-Dimensional Errors-in-Variables Models

Simulation-Selection-Extrapolation: Estimation in High-Dimensional Errors-in-Variables Models

Errors-in-variables models with dependent measurements

Gene Expression Imputation with Generative Adversarial Imputation Nets

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