3.Move βj from0 towards its least-squares coefficient <xj , r>,until some othercompetitor xk hasas much correlation with the current residual asdoes xj .
4.Move βj and βk in the directiondefined by their joint least squares coefficient ofthe current residual on (xj , xk),until some other competitor xl hasas much correlation with the current residual.
5.Continue in this way until all p predictorshave been entered. After min(N − 1, p)steps, we arrive at the full least-squares solution.
继续沿着这种方式前进,直到所有的p个变量都已经加入活动集。
最终,所有变量都被选中,且残差向量r垂直于所以变量,求得最小二乘解。
3 LARS算法的几何意义
Suppose Ak is the activeset of variables at the beginning of the kth step, and let βAk be thecoefficient vector for these variables at this step; there will be k −1 nonzerovalues, and the one just entered will be zero. If rk= y−XAkβAkis the currentresidual, then the direction for this step is
The coefficientprofile then evolves as βAk (α) = βAk+α · δk. Exercise 3.23 verifies that the directions chosen in this fashion dowhat is claimed: keep the correlations tied and decreasing. If the fit vectorat the beginning of this step is ˆfk, then itevolves as ˆfk(α) = fk+ α · uk, where uk= XAkδk is the new fit direction. The name “least angle” arisesfrom a geometrical interpretation of this process; uk makes thesmallest (and equal) angle with each of the predictors in Ak (Exercise 3.24).
Lasso estimate的提出是Tibshirani在1996年JRSSB上的一篇文章Regressionshrinkage and selection via lasso。所谓lasso,其全称是least absolute shrinkage and selection operator。其想法可以用如下的最优化问题来表述:
c++ 静态函数_c语言if结构格式1、对象与对象之间的成员变量是相互独立的.要想共用数据,则需要使用静态成员或静态方法2、只要在类中声明静态成员变量,即使不定义对象,也可以为静态成员变量分配空间,进而可以使用静态成员变量.(因为静态成员变量在对象创建之前就已经被分配了内存空间)3、静态成员变量虽然在类中,但它并不是随对象的建立而分配空间的,也不是随对象的撤销而释放(一般的成员在对象建立时会分配空间,在对象撤销时会释放…