Positive data are very common in many scientific fields and applications;for these data,it is known that estimation and inference based on relative error criterion are superior to that of absolute error criterion.In p...Positive data are very common in many scientific fields and applications;for these data,it is known that estimation and inference based on relative error criterion are superior to that of absolute error criterion.In prediction problems,conformal prediction provides a useful framework to construct flexible prediction intervals based on hypothesis testing,which has been actively studied in the past decade.In view of the advantages of the relative error criterion for regression problems with positive responses,in this paper,we combine the relative error criterion(REC)with conformal prediction to develop a novel REC-based predictive inference method to construct prediction intervals for the positive response.The proposed method satisfies the finite sample global coverage guarantee and to some extent achieves the local validity.We conduct extensive simulation studies and two real data analysis to demonstrate the competitiveness of the new proposed method.展开更多
In this paper,we develop an inexact symmetric proximal alternating direction method of multipliers(ISPADMM)with two convex combinations(ISPADMM-tcc)for solving two-block separable convex optimization problems with lin...In this paper,we develop an inexact symmetric proximal alternating direction method of multipliers(ISPADMM)with two convex combinations(ISPADMM-tcc)for solving two-block separable convex optimization problems with linear equality constraints.Specifically,the convex combination technique is incorporated into the proximal centers of both subproblems.We then approximately solve these two subproblems based on relative error criteria.The global convergence,and O(1/N)ergodic sublinear convergence rate measured by the function value residual and constraint violation are established under some mild conditions,where N denotes the number of iterations.Finally,numerical experiments on solving the l1-regularized analysis sparse recovery and the elastic net regularization regression problems illustrate the feasibility and effectiveness of the proposed method.展开更多
文摘Positive data are very common in many scientific fields and applications;for these data,it is known that estimation and inference based on relative error criterion are superior to that of absolute error criterion.In prediction problems,conformal prediction provides a useful framework to construct flexible prediction intervals based on hypothesis testing,which has been actively studied in the past decade.In view of the advantages of the relative error criterion for regression problems with positive responses,in this paper,we combine the relative error criterion(REC)with conformal prediction to develop a novel REC-based predictive inference method to construct prediction intervals for the positive response.The proposed method satisfies the finite sample global coverage guarantee and to some extent achieves the local validity.We conduct extensive simulation studies and two real data analysis to demonstrate the competitiveness of the new proposed method.
基金supported by the National Natural Science Foundation of China(12171106)the Guangxi Science and Technology Program(AD23023001)+4 种基金the Natural Science Foundation of Guangxi Province(2023GXNSFBA026029)the National Natural Science Foundation of China(12401403,12361063)the Research Project of Guangxi Minzu University(2022KJQD03)the Middle-aged and Young Teachers’Basic Ability Promotion Project of Guangxi Province(2023KY0168)the Xiangsihu Young Scholars Innovative Research Team of Guangxi Minzu University(2022GXUNXSHQN04).
文摘In this paper,we develop an inexact symmetric proximal alternating direction method of multipliers(ISPADMM)with two convex combinations(ISPADMM-tcc)for solving two-block separable convex optimization problems with linear equality constraints.Specifically,the convex combination technique is incorporated into the proximal centers of both subproblems.We then approximately solve these two subproblems based on relative error criteria.The global convergence,and O(1/N)ergodic sublinear convergence rate measured by the function value residual and constraint violation are established under some mild conditions,where N denotes the number of iterations.Finally,numerical experiments on solving the l1-regularized analysis sparse recovery and the elastic net regularization regression problems illustrate the feasibility and effectiveness of the proposed method.
