本文選題：Lasso + Adaptive-lasso　； 參考：《東北師范大學》2017年碩士論文

【摘要】：在Bradley Efron等人提出關于Lasso估計的最小角回歸(Least Angle Regression)算法后,使得關于Lasso的參數(shù)估計應用的更加廣泛,隨后Zou提出對Lasso進行改進后的Adaptive-lasso估計,Adaptive-lasso估計對每個參數(shù)實行了不同程度的壓縮,并且在理論方法具有哲人性質,因此本文考慮在某些特定情況下,我們不僅知道關于樣本的數(shù)據(jù)信息,還知道除了樣本信息外的一些先驗參數(shù)情況,如果能合理利用先驗情況中的參數(shù)約束條件,就可以提高參數(shù)估計的精確性,并且改善顯著性變量選擇的結果,于是選擇在Zou提出的Adaptive-lasso基礎上,對其添加線性約束,線性約束條件幾乎涵蓋了現(xiàn)實生活中較為普遍的先驗信息,這樣可以使得添加線性約束后的Adaptive-lasso應用的更加廣泛.在第三章中,我們給出了添加線性約束后的Adaptive-lasso定義,并利用拉格朗日乘子寫出了原問題的拉格朗日形式,討論了相應的對偶問題,并利用KKT條件推導出參數(shù)估計(?)的表達式和擬合值(?)的表達式以及原始解(?)和對偶解(?),(?),(?)的關系表達式,最后寫出該問題的坐標下降算法,并利用該算法進行計算機模擬實驗,證明在某些情況下添加線性約束后的Adaptive-lasso估計比原來沒有添加線性約束的Adaptive-lasso方法有更少的參數(shù)估計誤差,具有優(yōu)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.
【學位授予單位】：東北師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O212.1

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本文編號：1798934