具有线性约束的Adaptive-lasso

发布时间：2018-04-25 00:22

本文选题：Lasso + Adaptive-lasso　；参考：《东北师范大学》2017年硕士论文

【摘要】：在Bradley Efron等人提出关于Lasso估计的最小角回归(Least Angle Regression)算法后,使得关于Lasso的参数估计应用的更加广泛,随后Zou提出对Lasso进行改进后的Adaptive-lasso估计,Adaptive-lasso估计对每个参数实行了不同程度的压缩,并且在理论方法具有哲人性质,因此本文考虑在某些特定情况下,我们不仅知道关于样本的数据信息,还知道除了样本信息外的一些先验参数情况,如果能合理利用先验情况中的参数约束条件,就可以提高参数估计的精确性,并且改善显著性变量选择的结果,于是选择在Zou提出的Adaptive-lasso基础上,对其添加线性约束,线性约束条件几乎涵盖了现实生活中较为普遍的先验信息,这样可以使得添加线性约束后的Adaptive-lasso应用的更加广泛.在第三章中,我们给出了添加线性约束后的Adaptive-lasso定义,并利用拉格朗日乘子写出了原问题的拉格朗日形式,讨论了相应的对偶问题,并利用KKT条件推导出参数估计(?)的表达式和拟合值(?)的表达式以及原始解(?)和对偶解(?),(?),(?)的关系表达式,最后写出该问题的坐标下降算法,并利用该算法进行计算机模拟实验,证明在某些情况下添加线性约束后的Adaptive-lasso估计比原来没有添加线性约束的Adaptive-lasso方法有更少的参数估计误差,具有优越性。
[Abstract]:After Bradley Efron et al put forward the least angle regression Angle regress algorithm about Lasso estimation, it makes the parameter estimation of Lasso more widely used. Then Zou proposed that the modified Adaptive-lasso estimation of Lasso, Adaptive-lasso estimate, compresses each parameter to some extent, and has the character of philosopher in theory and method, so this paper considers that under certain circumstances, We not only know the data information about the sample, but also know some priori parameters except the sample information. If we can make use of the constraints of the parameters in the priori situation, we can improve the accuracy of the parameter estimation. And improve the result of significant variable selection, so choose to add linear constraints on the basis of Adaptive-lasso proposed by Zou. The linear constraints almost cover the more common prior information in real life. In this way, the Adaptive-lasso with linear constraints can be applied more widely. In chapter 3, we give the definition of Adaptive-lasso with linear constraints, and use Lagrange multiplier to write the Lagrangian form of the original problem, discuss the corresponding dual problem, and deduce the parameter estimation by using KKT condition. The expression and fitting value of the And the original solution And the dual solution. Finally, the coordinate descent algorithm of the problem is written, and the computer simulation experiment is carried out by using the algorithm. It is proved that in some cases the Adaptive-lasso estimation with linear constraints has less parameter estimation errors than the original Adaptive-lasso method without linear constraints.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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