地理加权回归中的参数估计

Juan Luo
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引用次数: 2

摘要

提出并实现了一个回归框架,它扩展了编程语言Java的回归分析,即对函数进行参数估计的能力。回归框架的独特之处在于回归分析的函数形式被表示为Java程序,其中一些参数不是先验已知的,而是需要从作为输入提供的训练集中学习。该回归框架的典型应用包括计算过程参数的校准,称为OO程序。为了实现回归学习,该框架的编译器(1)分析表示函数形式的参数化Java程序的结构;(2)自动生成约束优化问题,其中约束变量为未知参数,要最小化的目标函数为与训练集的误差平方和;(3)使用外部非线性优化求解器求解优化问题。然后,框架作为常规Java程序执行,其中最初未知的参数被找到的最优值替换。回归框架的语法和语义被正式定义,并在地理加权回归模型中举例说明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Parameter estimation in geographically weighted regression
Proposed and implemented is a regression framework, which extends the programming language Java with regression analysis, i.e., the capability to do parameter estimation for a function. The regression framework is unique in that functional forms for regression analysis are expressed as Java programs, in which some parameters are not a priori known, but need to be learned from training sets provided as input. Typical applications of this regression framework include calibration of parameters of computational processes, described as OO programs. To implement regression learning, the compiler of this framework (1) analyses the structure of the parameterized Java program that represents a functional form, (2) automatically generates a constraint optimization problem, in which constraint variables are the unknown parameters, and the objective function to be minimized is the sum of squares of errors with regarding to the training set, and (3) solves the optimization problem using an external nonlinear optimization solver. Then the framework executes as a regular Java program, in which the initially unknown parameters are replaced with the found optimal values. The syntax and semantics of the regression framework are formally defined and exemplified in the geographically weighted regression model.
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