In this paper,by combining the inertial technique and the gradient descent method with Polyak's stepsizes,we propose a novel inertial self-adaptive gradient algorithm to solve the split feasi-bility problem in Hil...In this paper,by combining the inertial technique and the gradient descent method with Polyak's stepsizes,we propose a novel inertial self-adaptive gradient algorithm to solve the split feasi-bility problem in Hilbert spaces and prove some strong and weak convergence theorems of our method under standard assumptions.We examine the performance of our method on the sparse recovery prob-lem beside an example in an infinite dimensional Hilbert space with synthetic data and give some numerical results to show the potential applicability of the proposed method and comparisons with related methods emphasize it further.展开更多
Multilevel (hierarchical) modeling is a generalization of linear and generalized linear modeling in which regression coefcients are modeled through a model,whose parameters are also estimated from data.Multilevel mode...Multilevel (hierarchical) modeling is a generalization of linear and generalized linear modeling in which regression coefcients are modeled through a model,whose parameters are also estimated from data.Multilevel model fails to fit well typically by the use of the EM algorithm once one of level error variance (like Cauchy distribution) tends to infinity.This paper proposes a composite multilevel to combine the nested structure of multilevel data and the robustness of the composite quantile regression,which greatly improves the efciency and precision of the estimation.The new approach,which is based on the Gauss-Seidel iteration and takes a full advantage of the composite quantile regression and multilevel models,still works well when the error variance tends to infinity.We show that even the error distribution is normal,the MSE of the estimation of composite multilevel quantile regression models nearly equals to mean regression.When the error distribution is not normal,our method still enjoys great advantages in terms of estimation efciency.展开更多
基金The National Natural Science Foundation of China(1117122161403255)+6 种基金the Doctoral Program Foundation of Institutions of Higher Education of China(20123120110004)the China Coal Industry Association 2011 Annual Scientific and Technical Guidance Programs(MTKJ-2011-404)the Natural Science Foundation of Shanghai(14ZR1429200)the Shanghai Leading Academic Discipline Project(XTK X2012)the Innovation Program of Shanghai Municipal Education Commission(15ZZ073)the Doctoral Starting Projection of the University of Shanghai for Science and Technology(ID-10-303-002)the Young Teacher Training Projection Program of Shanghai for Science and Technology
基金funded by University of Transport and Communications (UTC) under Grant Number T2023-CB-001
文摘In this paper,by combining the inertial technique and the gradient descent method with Polyak's stepsizes,we propose a novel inertial self-adaptive gradient algorithm to solve the split feasi-bility problem in Hilbert spaces and prove some strong and weak convergence theorems of our method under standard assumptions.We examine the performance of our method on the sparse recovery prob-lem beside an example in an infinite dimensional Hilbert space with synthetic data and give some numerical results to show the potential applicability of the proposed method and comparisons with related methods emphasize it further.
基金The work was partially supported by Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(No.10XNL018)
文摘Multilevel (hierarchical) modeling is a generalization of linear and generalized linear modeling in which regression coefcients are modeled through a model,whose parameters are also estimated from data.Multilevel model fails to fit well typically by the use of the EM algorithm once one of level error variance (like Cauchy distribution) tends to infinity.This paper proposes a composite multilevel to combine the nested structure of multilevel data and the robustness of the composite quantile regression,which greatly improves the efciency and precision of the estimation.The new approach,which is based on the Gauss-Seidel iteration and takes a full advantage of the composite quantile regression and multilevel models,still works well when the error variance tends to infinity.We show that even the error distribution is normal,the MSE of the estimation of composite multilevel quantile regression models nearly equals to mean regression.When the error distribution is not normal,our method still enjoys great advantages in terms of estimation efciency.
