scholarly journals Communication-Efficient Modeling with Penalized Quantile Regression for Distributed Data

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Aijun Hu ◽  
Chujin Li ◽  
Jing Wu
Keyword(s):  
Quantile Regression ◽  
Estimation Error ◽  
Asymptotic Properties ◽  
High Dimensional ◽  
Distributed Data ◽  
Local Data ◽  
High Dimensional Case ◽  
Alternating Direction ◽  
Admm Algorithm ◽  
Resistance Data

In order to deal with high-dimensional distributed data, this article develops a novel and communication-efficient approach for sparse and high-dimensional data with the penalized quantile regression. In each round, the proposed method only requires the master machine to deal with a sparse penalized quantile regression which could be realized fastly by proximal alternating direction method of multipliers (ADMM) algorithm and the other worker machines to compute the subgradient on local data. The advantage of the proximal ADMM algorithm is that it could make every parameter of iteration to have closed formula even in high-dimensional case, which greatly improves the speed of calculation. As for the communication efficiency, the proposed method does not sacrifice any statistical accuracy and provably improves the estimation error obtained by centralized method, provided the penalty levels are chosen properly. Moreover, the asymptotic properties of the proposed estimation and the convergence of the algorithm are convincible. Especially, it presents extensive experiments on both the numerical simulations and the HIV drug resistance data analysis, which all confirm the significant efficiency of our proposed method in quantile regression for distributed data by comparative and empirical analysis.

scholarly journals Quantile Regression with Generated Regressors

Econometrics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 16
Author(s):  
Liqiong Chen ◽  
Antonio F. Galvao ◽  
Suyong Song
Keyword(s):  
Quantile Regression ◽  
Estimation Error ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Estimation Procedure ◽  
Finite Sample ◽  
Testing Procedures ◽  
Engel Curves ◽  
Generated Regressors ◽  
Two Step Estimation

This paper studies estimation and inference for linear quantile regression models with generated regressors. We suggest a practical two-step estimation procedure, where the generated regressors are computed in the first step. The asymptotic properties of the two-step estimator, namely, consistency and asymptotic normality are established. We show that the asymptotic variance-covariance matrix needs to be adjusted to account for the first-step estimation error. We propose a general estimator for the asymptotic variance-covariance, establish its consistency, and develop testing procedures for linear hypotheses in these models. Monte Carlo simulations to evaluate the finite-sample performance of the estimation and inference procedures are provided. Finally, we apply the proposed methods to study Engel curves for various commodities using data from the UK Family Expenditure Survey. We document strong heterogeneity in the estimated Engel curves along the conditional distribution of the budget share of each commodity. The empirical application also emphasizes that correctly estimating confidence intervals for the estimated Engel curves by the proposed estimator is of importance for inference.

Fast Algorithms for LS and LAD-Collaborative Regression

2021 ◽  
Author(s):  
Jun Sun ◽  
Lingchen Kong ◽  
Mei Li
Keyword(s):  
Numerical Experiments ◽  
Modern Science ◽  
Alternating Direction Method ◽  
Least Square ◽  
High Dimensional ◽  
Statistical Interpretation ◽  
Absolute Deviation ◽  
Linear Rate ◽  
Alternating Direction ◽  
High Dimensional Datasets

With the development of modern science and technology, it is easy to obtain a large number of high-dimensional datasets, which are related but different. Classical unimodel analysis is less likely to capture potential links between the different datasets. Recently, a collaborative regression model based on least square (LS) method for this problem has been proposed. In this paper, we propose a robust collaborative regression based on the least absolute deviation (LAD). We give the statistical interpretation of the LS-collaborative regression and LAD-collaborative regression. Then we design an efficient symmetric Gauss–Seidel-based alternating direction method of multipliers algorithm to solve the two models, which has the global convergence and the Q-linear rate of convergence. Finally we report numerical experiments to illustrate the efficiency of the proposed methods.

Functional Linear Regression

2018 ◽  
Author(s):  
Hervé Cardot ◽  
Pascal Sarda
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Estimation Error ◽  
Asymptotic Properties ◽  
Principal Component Regression ◽  
Principal Component ◽  
Penalized Least Squares ◽  
Open Problems ◽  
Functional Linear Regression

This article presents a selected bibliography on functional linear regression (FLR) and highlights the key contributions from both applied and theoretical points of view. It first defines FLR in the case of a scalar response and shows how its modelization can also be extended to the case of a functional response. It then considers two kinds of estimation procedures for this slope parameter: projection-based estimators in which regularization is performed through dimension reduction, such as functional principal component regression, and penalized least squares estimators that take into account a penalized least squares minimization problem. The article proceeds by discussing the main asymptotic properties separating results on mean square prediction error and results on L2 estimation error. It also describes some related models, including generalized functional linear models and FLR on quantiles, and concludes with a complementary bibliography and some open problems.

scholarly journals High-dimensional Log-Error-in-Variable Regression with Applications to Microbial Compositional Data Analysis

Biometrika ◽  
2021 ◽  
Author(s):  
Pixu Shi ◽  
Yuchen Zhou ◽  
Anru R Zhang
Keyword(s):  
Data Analysis ◽  
Compositional Data ◽  
Estimation Error ◽  
Real Data ◽  
Upper And Lower Bounds ◽  
High Dimensional ◽  
Compositional Data Analysis ◽  
Sequencing Data ◽  
Contrast Model ◽  
Critical Issues

Abstract In microbiome and genomic studies, the regression of compositional data has been a crucial tool for identifying microbial taxa or genes that are associated with clinical phenotypes. To account for the variation in sequencing depth, the classic log-contrast model is often used where read counts are normalized into compositions. However, zero read counts and the randomness in covariates remain critical issues. In this article, we introduce a surprisingly simple, interpretable, and efficient method for the estimation of compositional data regression through the lens of a novel high-dimensional log-error-in-variable regression model. The proposed method provides both corrections on sequencing data with possible overdispersion and simultaneously avoids any subjective imputation of zero read counts. We provide theoretical justifications with matching upper and lower bounds for the estimation error. The merit of the procedure is illustrated through real data analysis and simulation studies.

Extensions to Quantile Regression Forests for Very High-Dimensional Data

2014 ◽  
pp. 247-258 ◽  
Author(s):  
Nguyen Thanh Tung ◽  
Joshua Zhexue Huang ◽  
Imran Khan ◽  
Mark Junjie Li ◽  
Graham Williams
Keyword(s):  
Quantile Regression ◽  
High Dimensional Data ◽  
High Dimensional ◽  
Very High

An Inexact Projected Gradient Method for Sparsity-Constrained Quadratic Measurements Regression

2019 ◽  
Vol 36 (02) ◽  
pp. 1940008
Author(s):  
Jun Fan ◽  
Liqun Wang ◽  
Ailing Yan
Keyword(s):  
Gradient Method ◽  
Least Squares Method ◽  
Optimal Solution ◽  
High Dimensional ◽  
Sparse Signals ◽  
Projected Gradient Method ◽  
Constrained Least Squares ◽  
Projected Gradient ◽  
High Dimensional Case ◽  
Noisy Measurements

In this paper, we employ the sparsity-constrained least squares method to reconstruct sparse signals from the noisy measurements in high-dimensional case, and derive the existence of the optimal solution under certain conditions. We propose an inexact sparse-projected gradient method for numerical computation and discuss its convergence. Moreover, we present numerical results to demonstrate the efficiency of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document