保序回归算法的MATLAB实现  

MATLAB implementation of isotonic regression algorithm

作　　者：刘瑞银[1] 周志慧 杜欢[1] LIU Ruiyin;ZHOU Zhihui;DU Huan(College of Mathematics and Systems Science,Shenyang Normal University,Shenyang 110034,China)

机构地区：[1]沈阳师范大学数学与系统科学学院,沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2022年第6期509-513,共5页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11401393);辽宁省科技厅自然科学基金资助项目(LJC201914)。

摘　　要：针对简单半序和伞型半序的保序回归问题,采用PAVA(pool-adjacent-violators)算法及其变换分别对2种半序进行求解。首先,阐述保序函数及保序回归的定义,列举保序回归中常见的序关系;其次,介绍求解简单半序及伞型半序保序回归的算法,并给出2种算法的具体应用实例;再次,利用MATLAB(matrix&laboratory)软件编写2个自定义函数Iso和Umb分别求解简单半序和伞型半序的保序回归;最后,将这2个自定义函数应用于实例中。得到的结果与实例中的实际结果相一致,说明编写的2个自定义函数对于解决简单半序和伞型半序的保序回归问题切实可行,并且这2个函数可以简单快速地解决满足这2种序关系的问题,为后续研究其他保序回归相关问题奠定了理论依据。For the isotonic regression problems of simple order and umbrella order, PAVA algorithm and its transformation are used to solve the two orders respectively. Firstly, the definitions of isotonic function and isotonic regression are expounded, and the common order relations in isotonic regression are listed;Secondly, the algorithms for solving simple order and umbrella isotonic regression are introduced, and the specific application examples of the two algorithms are given;Then, two user-defined functions Iso and Umb are written by MATLAB software to solve the isotonic regression of simple order and umbrella order respectively;Finally, the two user-defined functions are applied to the example, and the results are consistent with the actual results in the example, which shows that the two user-defined functions are feasible in solving the isotonic regression problems of simple order and umbrella order, and the two functions can simply and quickly solve the problems that meet the two order relations, which lays an experimental foundation for the follow-up study of other isotonic regression related problems.

关 键 词：保序回归 简单半序 伞型半序 PAVA算法 

分 类 号：O212.3[理学—概率论与数理统计]