对于非光滑强凸问题,在线梯度下降(Online Gradient Decent,OGD)取适当步长参数可以得到对数阶后悔界.然而,这并不能使一阶随机优化算法达到最优收敛速率.为解决这一问题,研究者通常采取两种方案:其一是改进算法本身,另一种是修改算法...对于非光滑强凸问题,在线梯度下降(Online Gradient Decent,OGD)取适当步长参数可以得到对数阶后悔界.然而,这并不能使一阶随机优化算法达到最优收敛速率.为解决这一问题,研究者通常采取两种方案:其一是改进算法本身,另一种是修改算法输出方式.典型的Adam(Adaptive moment estimation)型算法SAdam(Strongly convex Adaptive moment esti⁃mation)采用了改进算法的方式,并添加了自适应步长策略和动量技巧,虽然得到更好的数据依赖的后悔界,但在随机情形仍然达不到最优.针对这个问题,本文改用加权平均的算法输出方式,并且重新设计与以往算法同阶的步长超参数,提出了一种名为WSAdam(Weighted average Strongly convex Adaptive moment estimation)的Adam型算法.证明了WSAdam达到了非光滑强凸问题的最优收敛速率.经过Reddi问题的测试和在非光滑强凸函数优化中的实验,验证了所提方法的有效性.展开更多
Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the fir...Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function.展开更多
文摘对于非光滑强凸问题,在线梯度下降(Online Gradient Decent,OGD)取适当步长参数可以得到对数阶后悔界.然而,这并不能使一阶随机优化算法达到最优收敛速率.为解决这一问题,研究者通常采取两种方案:其一是改进算法本身,另一种是修改算法输出方式.典型的Adam(Adaptive moment estimation)型算法SAdam(Strongly convex Adaptive moment esti⁃mation)采用了改进算法的方式,并添加了自适应步长策略和动量技巧,虽然得到更好的数据依赖的后悔界,但在随机情形仍然达不到最优.针对这个问题,本文改用加权平均的算法输出方式,并且重新设计与以往算法同阶的步长超参数,提出了一种名为WSAdam(Weighted average Strongly convex Adaptive moment estimation)的Adam型算法.证明了WSAdam达到了非光滑强凸问题的最优收敛速率.经过Reddi问题的测试和在非光滑强凸函数优化中的实验,验证了所提方法的有效性.
文摘Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function.
