When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are func...When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .展开更多
When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are func...When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .展开更多
Deficiencies of the performance-based iterative learning control （ILC） for the non-regular systems are investigated in detail, then a faster control input updating and lifting technique is introduced in the design o...Deficiencies of the performance-based iterative learning control （ILC） for the non-regular systems are investigated in detail, then a faster control input updating and lifting technique is introduced in the design of performance index based ILCs for the partial non-regular systems. Two ldnds of optimal ILCs based on different performance indices are considered. Finally, simulation examples are given to illustrate the feasibility of the proposed learning controls.展开更多
A method to construct strongly non regular order bounded operators from a classical Banach lattice C into any separable Banach lattice F without Dedekind σ completeness is presented in this paper. A r...A method to construct strongly non regular order bounded operators from a classical Banach lattice C into any separable Banach lattice F without Dedekind σ completeness is presented in this paper. A result concerning the order bounded norm and the regular norm is also contained.展开更多
For any given 0 〈α 〈 β 〈 ∞, we construct a tree such that under tree metric, the Hausdorff dimension of the corresponding boundary is α, but both the Packing dimension and the boxing dimension are β. Applying ...For any given 0 〈α 〈 β 〈 ∞, we construct a tree such that under tree metric, the Hausdorff dimension of the corresponding boundary is α, but both the Packing dimension and the boxing dimension are β. Applying the connection between tree and iterated functions system, non- regular fractal sets on real line are constructed. Moreover, the method adopted in our paper is different from those which have been used before for constructing non-regular fractal set in general metric space.展开更多
个性化联邦学习侧重于为各客户端提供个性化模型,旨在提高对异构数据的处理性能,然而现有的个性化联邦学习算法大多以增加客户端参数量为代价提高个性化模型的性能,使计算变得复杂.为了解决此问题,文中提出基于稀疏正则双层优化的个性...个性化联邦学习侧重于为各客户端提供个性化模型,旨在提高对异构数据的处理性能,然而现有的个性化联邦学习算法大多以增加客户端参数量为代价提高个性化模型的性能,使计算变得复杂.为了解决此问题,文中提出基于稀疏正则双层优化的个性化联邦学习算法(Personalized Federated Learning Based on Sparsity Regularized Bi-level Optimization,pFedSRB),在客户端的个性化更新中引入l 1范数稀疏正则化,提升个性化模型的稀疏度,避免不必要的客户端参数更新,降低模型复杂度.将个性化联邦学习建模为双层优化问题,内层优化采用交替方向乘子法,可提高学习速度.在4个联邦学习基准数据集上的实验表明,pFedSRB在异构数据上表现出色,在提高模型性能的同时有效降低训练用时和空间成本.展开更多
文摘When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .
文摘When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .
基金supported by the National Natural Science Foundation of China (No.60774023)Hunan Provincial Natural Science Foundation (No.06JJ50141)
文摘Deficiencies of the performance-based iterative learning control （ILC） for the non-regular systems are investigated in detail, then a faster control input updating and lifting technique is introduced in the design of performance index based ILCs for the partial non-regular systems. Two ldnds of optimal ILCs based on different performance indices are considered. Finally, simulation examples are given to illustrate the feasibility of the proposed learning controls.
文摘A method to construct strongly non regular order bounded operators from a classical Banach lattice C into any separable Banach lattice F without Dedekind σ completeness is presented in this paper. A result concerning the order bounded norm and the regular norm is also contained.
文摘For any given 0 〈α 〈 β 〈 ∞, we construct a tree such that under tree metric, the Hausdorff dimension of the corresponding boundary is α, but both the Packing dimension and the boxing dimension are β. Applying the connection between tree and iterated functions system, non- regular fractal sets on real line are constructed. Moreover, the method adopted in our paper is different from those which have been used before for constructing non-regular fractal set in general metric space.
文摘个性化联邦学习侧重于为各客户端提供个性化模型,旨在提高对异构数据的处理性能,然而现有的个性化联邦学习算法大多以增加客户端参数量为代价提高个性化模型的性能,使计算变得复杂.为了解决此问题,文中提出基于稀疏正则双层优化的个性化联邦学习算法(Personalized Federated Learning Based on Sparsity Regularized Bi-level Optimization,pFedSRB),在客户端的个性化更新中引入l 1范数稀疏正则化,提升个性化模型的稀疏度,避免不必要的客户端参数更新,降低模型复杂度.将个性化联邦学习建模为双层优化问题,内层优化采用交替方向乘子法,可提高学习速度.在4个联邦学习基准数据集上的实验表明,pFedSRB在异构数据上表现出色,在提高模型性能的同时有效降低训练用时和空间成本.
