lasso and ridge regression

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lasso and ridge regression

Gafar Matanmi Oyeyemi
Dear All

The problem is about regularization methods in multiple regression when the
independent variables are collinear. A modified regularization method with
two tuning parameters l1 and l2 and their product l1*l2 (Lambda 1 and
Lambda 2) such that l1 takes care of ridge property and l2 takes care of
LASSO property is proposed

The proposed method is given
<https://i.stack.imgur.com/Ta8FR.jpg>

The problem is how to adapt "glmnet" to accomplish our task.

The extract of the code used is reproduced as follows;

    cv.ridge<- glmnet(x, y, family="gaussian", alpha=0,
    lambda=lambda1, standardize=TRUE)
    cv.lasso<- glmnet(x, y, family="gaussian", alpha=1,
    lambda=lambda2, standardize=TRUE)
    ##weight
    a=1/abs(matrix(coef(cv.ridge, s=lambda1)[, 1][2:(ncol(x)+1)]
    ))^1
    b=1/abs(matrix(coef(cv.lasso, s=lambda2)[, 1][2:(ncol(x)+1)]
    ))^1
    c=a*b
    w4 <-a+b+c
    w4[w4[,1] == Inf] <- 9
    # Fit modified procedure
    fit<- glmnet(x, y, family="gaussian",
    alpha=alpha,lambda=lambda1+lambda2, penalty.factor=w4)

The question is; Does the code address the modified procedure in as shown
in the equation? If not, suggestions are please welcome.

Thanks


--
OYEYEMI, Gafar Matanmi (Ph.D)
Reader
Department of Statistics
University of Ilorin.
Area of Specialization: Multivariate Analysis, Statistical Quality Control
& Total Quality Management.
Tel: +2348052278655, +2348068241885

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