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    1. Full lasso

set.seed(999) cv.full <- cv.glmnet(x, ly, family='binomial', alpha=1, parallel=TRUE) plot(cv.full) # cross-validation curve and two lambda's plot(glmnet(x, ly, family='binomial', alpha=1), xvar="lambda", label=TRUE) # coefficient path plot plot(glmnet(x, ly, family='binomial', alpha=1)) # L1 norm plot log(cv.full$lambda.min) # -4.546394 log(cv.full$lambda.1se) # -3.61605 sum(coef(cv.full, s=cv.full$lambda.min) != 0) # 44

    1. Ridge Regression to create the Adaptive Weights Vector

set.seed(999) cv.ridge <- cv.glmnet(x, ly, family='binomial', alpha=0, parallel=TRUE) wt <- 1/abs(matrix(coef(cv.ridge, s=cv.ridge$lambda.min)

                  [, 1][2:(ncol(x)+1)] ))^1 ## Using gamma = 1, exclude intercept
    1. Adaptive Lasso using the 'penalty.factor' argument

set.seed(999) cv.lasso <- cv.glmnet(x, ly, family='binomial', alpha=1, parallel=TRUE, penalty.factor=wt)

  1. defautl type.measure="deviance" for logistic regression

plot(cv.lasso) log(cv.lasso$lambda.min) # -2.995375 log(cv.lasso$lambda.1se) # -0.7625655 sum(coef(cv.lasso, s=cv.lasso$lambda.min) != 0) # 34 </syntaxhighlight>

Lasso logistic regression

https://freakonometrics.hypotheses.org/52894

Lagrange Multipliers

A Simple Explanation of Why Lagrange Multipliers Works

How to solve lasso/convex optimization