scholarly journals Group Identification and Variable Selection in Quantile Regression

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Ali Alkenani ◽  
Basim Shlaibah Msallam
Keyword(s):  
Variable Selection ◽  
Quantile Regression ◽  
Group Identification ◽  
Real Data ◽  
True Model

Using the Pairwise Absolute Clustering and Sparsity (PACS) penalty, we proposed the regularized quantile regression QR method (QR-PACS). The PACS penalty achieves the elimination of insignificant predictors and the combination of predictors with indistinguishable coefficients (IC), which are the two issues raised in the searching for the true model. QR-PACS extends PACS from mean regression settings to QR settings. The paper shows that QR-PACS can yield promising predictive precision as well as identifying related groups in both simulation and real data.

scholarly journals Robust Group Identification and Variable Selection in Regression

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Ali Alkenani ◽  
Tahir R. Dikheel
Keyword(s):  
Variable Selection ◽  
Least Squares ◽  
Loss Function ◽  
Simulation Study ◽  
Group Identification ◽  
Real Data ◽  
True Model ◽  
Mm Estimation

The elimination of insignificant predictors and the combination of predictors with indistinguishable coefficients are the two issues raised in searching for the true model. Pairwise Absolute Clustering and Sparsity (PACS) achieves both goals. Unfortunately, PACS is sensitive to outliers due to its dependency on the least-squares loss function which is known to be very sensitive to unusual data. In this article, the sensitivity of PACS to outliers has been studied. Robust versions of PACS (RPACS) have been proposed by replacing the least squares and nonrobust weights in PACS with MM-estimation and robust weights depending on robust correlations instead of person correlation, respectively. A simulation study and two real data applications have been used to assess the effectiveness of the proposed methods.

scholarly journals Mixed effect modelling and variable selection for quantile regression

2021 ◽  
pp. 1471082X2110334
Author(s):  
Haim Bar ◽  
James G. Booth ◽  
Martin T. Wells
Keyword(s):  
Variable Selection ◽  
Em Algorithm ◽  
Quantile Regression ◽  
Weighted Least Squares ◽  
Age At Onset ◽  
Real Data ◽  
Riboflavin Production ◽  
Mixed Effect ◽  
Linear Predictor ◽  
Selection For

It is known that the estimating equations for quantile regression (QR) can be solved using an EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent generalized inverse-Gaussian variables. This fact is exploited here to extend QR to allow for random effects in the linear predictor. Convergence of the algorithm in this setting is established by showing that it is a generalized alternating minimization (GAM) procedure. Another modification of the EM algorithm also allows us to adapt a recently proposed method for variable selection in mean regression models to the QR setting. Simulations show that the resulting method significantly outperforms variable selection in QR models using the lasso penalty. Applications to real data include a frailty QR analysis of hospital stays, and variable selection for age at onset of lung cancer and for riboflavin production rate using high-dimensional gene expression arrays for prediction.

scholarly journals Variable Selection and Regularization in Quantile Regression via Minimum Covariance Determinant Based Weights

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 33
Author(s):  
Edmore Ranganai ◽  
Innocent Mudhombo
Keyword(s):  
Variable Selection ◽  
Quantile Regression ◽  
Data Sets ◽  
Least Absolute Deviation ◽  
Minimum Covariance Determinant ◽  
Absolute Deviation ◽  
Leverage Points ◽  
Influential Points ◽  
Computationally Intensive ◽  
Space Data

The importance of variable selection and regularization procedures in multiple regression analysis cannot be overemphasized. These procedures are adversely affected by predictor space data aberrations as well as outliers in the response space. To counter the latter, robust statistical procedures such as quantile regression which generalizes the well-known least absolute deviation procedure to all quantile levels have been proposed in the literature. Quantile regression is robust to response variable outliers but very susceptible to outliers in the predictor space (high leverage points) which may alter the eigen-structure of the predictor matrix. High leverage points that alter the eigen-structure of the predictor matrix by creating or hiding collinearity are referred to as collinearity influential points. In this paper, we suggest generalizing the penalized weighted least absolute deviation to all quantile levels, i.e., to penalized weighted quantile regression using the RIDGE, LASSO, and elastic net penalties as a remedy against collinearity influential points and high leverage points in general. To maintain robustness, we make use of very robust weights based on the computationally intensive high breakdown minimum covariance determinant. Simulations and applications to well-known data sets from the literature show an improvement in variable selection and regularization due to the robust weighting formulation.

scholarly journals Variable Selection via SCAD-Penalized Quantile Regression for High-Dimensional Count Data

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 153205-153216
Author(s):  
Dost Muhammad Khan ◽  
Anum Yaqoob ◽  
Nadeem Iqbal ◽  
Abdul Wahid ◽  
Umair Khalil ◽  
...  
Keyword(s):  
Variable Selection ◽  
Quantile Regression ◽  
Count Data ◽  
High Dimensional

scholarly journals Joint variable selection and network modeling for detecting eQTLs

2020 ◽  
Vol 19 (1) ◽  
Author(s):  
Xuan Cao ◽  
Lili Ding ◽  
Tesfaye B. Mersha
Keyword(s):  
Variable Selection ◽  
Multiple Testing ◽  
Bayes Factor ◽  
Graph Model ◽  
Real Data ◽  
Bayesian Regression ◽  
Joint Estimation ◽  
Eqtl Analysis ◽  
Multiple Testing Correction ◽  
Joint Variable

AbstractIn this study, we conduct a comparison of three most recent statistical methods for joint variable selection and covariance estimation with application of detecting expression quantitative trait loci (eQTL) and gene network estimation, and introduce a new hierarchical Bayesian method to be included in the comparison. Unlike the traditional univariate regression approach in eQTL, all four methods correlate phenotypes and genotypes by multivariate regression models that incorporate the dependence information among phenotypes, and use Bayesian multiplicity adjustment to avoid multiple testing burdens raised by traditional multiple testing correction methods. We presented the performance of three methods (MSSL – Multivariate Spike and Slab Lasso, SSUR – Sparse Seemingly Unrelated Bayesian Regression, and OBFBF – Objective Bayes Fractional Bayes Factor), along with the proposed, JDAG (Joint estimation via a Gaussian Directed Acyclic Graph model) method through simulation experiments, and publicly available HapMap real data, taking asthma as an example. Compared with existing methods, JDAG identified networks with higher sensitivity and specificity under row-wise sparse settings. JDAG requires less execution in small-to-moderate dimensions, but is not currently applicable to high dimensional data. The eQTL analysis in asthma data showed a number of known gene regulations such as STARD3, IKZF3 and PGAP3, all reported in asthma studies. The code of the proposed method is freely available at GitHub (https://github.com/xuan-cao/Joint-estimation-for-eQTL).

scholarly journals Variable Selection for Nonparametric Learning with Power Series Kernels

2019 ◽  
Vol 31 (8) ◽  
pp. 1718-1750
Author(s):  
Kota Matsui ◽  
Wataru Kumagai ◽  
Kenta Kanamori ◽  
Mitsuaki Nishikimi ◽  
Takafumi Kanamori
Keyword(s):  
Power Series ◽  
Variable Selection ◽  
Density Ratio ◽  
Target Function ◽  
Real Data ◽  
Adaptive Lasso ◽  
Text Type ◽  
Nonparametric Learning ◽  
Stage Estimation ◽  
Selection Consistency

In this letter, we propose a variable selection method for general nonparametric kernel-based estimation. The proposed method consists of two-stage estimation: (1) construct a consistent estimator of the target function, and (2) approximate the estimator using a few variables by [Formula: see text]-type penalized estimation. We see that the proposed method can be applied to various kernel nonparametric estimation such as kernel ridge regression, kernel-based density, and density-ratio estimation. We prove that the proposed method has the property of variable selection consistency when the power series kernel is used. Here, the power series kernel is a certain class of kernels containing polynomial and exponential kernels. This result is regarded as an extension of the variable selection consistency for the nonnegative garrote (NNG), a special case of the adaptive Lasso, to the kernel-based estimators. Several experiments, including simulation studies and real data applications, show the effectiveness of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document