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High-dimensional expectile regression incorporating graphical structure among predictors

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2023年第2期93卷 231-248页

作者： Pan, Yingli Zhao, Xiaoluo Wei, Sha Liu, Zhan Hubei Univ Fac Math & Stat Hubei Key Lab Appl Math Wuhan 430062 Peoples R China

With the extensive application of high-dimensional heterogeneous data in various disciplines, sparse expectile regression is increasingly favoured by people. In this paper, we make use of the graphical structure among predictors node-by-node to improve the performance of parameter estimation, model selection and prediction in sparse expectile regression. A modified alternating direction method of multipliers (admm) algorithm with a linearization trick is proposed to implement the proposed method numerically, and the convergence of the algorithm is proved. Simulation studies are conducted to evaluate the finite-sample performance of the proposed method. We demonstrate the practicability of the proposed approach with a dataset of the expression quantitative trait locus mapping (eQTL) experiment in Rattus norvegicus.

关键词： Heterogeneous data sparse expectile regression graphical structure modified admm algorithm

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Distributed optimization and statistical learning for large-scale penalized expectile regression

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JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2021年第1期50卷 290-314页

作者： Pan, Yingli Hubei Univ Fac Math & Stat Hubei Key Lab Appl Math Wuhan Peoples R China

Large-scale data from various research fields are not only heterogeneous and sparse but also difficult to store on a single machine. Expectile regression is a popular alternative for modeling heterogeneous data. In this paper, we devise a distributed optimization approach to SCAD and adaptive LASSO penalized expectile regression, where the observations are randomly partitioned across multiple machines. We construct a penalized communication-efficient surrogate loss (CSL) function. Computationally, our method based on the CSL function requires only the master machine to solve a regular M-estimation problem, while other worker machines compute the gradient of the loss function on local data. Our method matches the estimation error bound of the centralized method during consecutive rounds of communication. Under some mild assumptions, we establish the oracle properties of the SCAD and adaptive LASSO penalized expectile regression. We then develop a modified alternating direction method of multipliers (admm) algorithm for the implementation of the proposed estimator. A series of simulation studies are conducted to assess the finite-sample performance of the proposed estimator. Applications to an HIV study demonstrate the practicability of the proposed method.

关键词： Distributed optimization Expectile regression SCAD Adaptive LASSO modified admm algorithm

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