We consider a wide range of non-convex regularized minimization problems, where the non-convex regularization term is composite with a linear function engaged in sparse learning. Recent theoretical investigations have...We consider a wide range of non-convex regularized minimization problems, where the non-convex regularization term is composite with a linear function engaged in sparse learning. Recent theoretical investigations have demonstrated their superiority over their convex counterparts. The computational challenge lies in the fact that the proximal mapping associated with non-convex regularization is not easily obtained due to the imposed linear composition. Fortunately, the problem structure allows one to introduce an auxiliary variable and reformulate it as an optimization problem with linear constraints, which can be solved using the Linearized Alternating Direction Method of Multipliers （LADMM）. Despite the success of LADMM in practice, it remains unknown whether LADMM is convergent in solving such non-convex compositely regularized optimizations. In this research, we first present a detailed convergence analysis of the LADMM algorithm for solving a non-convex compositely regularized optimization problem with a large class of non-convex penalties. Furthermore, we propose an Adaptive LADMM （AdaLADMM） algorithm with a line-search criterion. Experimental results on different genres of datasets validate the efficacy of the proposed algorithm.展开更多
In this paper,we explore sparsity and homogeneity of regression coefficients incorporating prior constraint information.The sparsity means that a small fraction of regression coefficients is nonzero,and the homogeneit...In this paper,we explore sparsity and homogeneity of regression coefficients incorporating prior constraint information.The sparsity means that a small fraction of regression coefficients is nonzero,and the homogeneity means that regression coefficients are grouped and have exactly the same value in each group.A general pairwise fusion approach is proposed to deal with the sparsity and homogeneity detection when combining prior convex constraints.We develop a modified alternating direction method of multipliers algorithm to obtain the estimators and demonstrate its convergence.The efficiency of both sparsity and homogeneity detection can be improved by combining the prior information.Our proposed method is further illustrated by simulation studies and analysis of an ozone dataset.展开更多
基金supported by the National Natural Science Foundation of China(Nos.61303264,61202482,and 61202488)Guangxi Cooperative Innovation Center of Cloud Computing and Big Data(No.YD16505)Distinguished Young Scientist Promotion of National University of Defense Technology
文摘We consider a wide range of non-convex regularized minimization problems, where the non-convex regularization term is composite with a linear function engaged in sparse learning. Recent theoretical investigations have demonstrated their superiority over their convex counterparts. The computational challenge lies in the fact that the proximal mapping associated with non-convex regularization is not easily obtained due to the imposed linear composition. Fortunately, the problem structure allows one to introduce an auxiliary variable and reformulate it as an optimization problem with linear constraints, which can be solved using the Linearized Alternating Direction Method of Multipliers （LADMM）. Despite the success of LADMM in practice, it remains unknown whether LADMM is convergent in solving such non-convex compositely regularized optimizations. In this research, we first present a detailed convergence analysis of the LADMM algorithm for solving a non-convex compositely regularized optimization problem with a large class of non-convex penalties. Furthermore, we propose an Adaptive LADMM （AdaLADMM） algorithm with a line-search criterion. Experimental results on different genres of datasets validate the efficacy of the proposed algorithm.
文摘In this paper,we explore sparsity and homogeneity of regression coefficients incorporating prior constraint information.The sparsity means that a small fraction of regression coefficients is nonzero,and the homogeneity means that regression coefficients are grouped and have exactly the same value in each group.A general pairwise fusion approach is proposed to deal with the sparsity and homogeneity detection when combining prior convex constraints.We develop a modified alternating direction method of multipliers algorithm to obtain the estimators and demonstrate its convergence.The efficiency of both sparsity and homogeneity detection can be improved by combining the prior information.Our proposed method is further illustrated by simulation studies and analysis of an ozone dataset.
