2.5 Practical - LASSO

#lasso
Q6 LASSO In this question, the goal is to predict y from x. a) Load the workspace data.Rdata and show an informative plot of the y and x space. b) Run a 10-fold cross-validated LASSO logistic (family = "binomial") regression using the misclassification error as the criterion. c) Make a prediction of the class labels at 𝜆 = 0.05, 0.01 d) create a plot that shows the values of 𝜆. What is the optimal value and why?

#Load the workspace and plot y vs. x

load("data.Rdata")
plot(x, y, main="Scatterplot of y vs x", xlab="x", ylab="y")

#10-fold cross-validated LASSO logistic regression:
# Prepare data
X <- as.matrix(x)
Y <- y

# Fit the model with cross-validation
set.seed(123)  # For reproducibility
cv.lasso <- cv.glmnet(X, Y, family="binomial", alpha=1, nfolds=10)

#Predict class labels at 𝜆 = 0.05, 0.01:

To predict class labels, you can use the predict function with type="class". You can do this for both 𝜆 values:

predictions_0.05 <- predict(cv.lasso, newx=X, s=0.05, type="class")
predictions_0.01 <- predict(cv.lasso, newx=X, s=0.01, type="class")

#Plot showing values of 𝜆:

The cv.glmnet object has a built-in plot method that shows the mean and standard deviation of the misclassification error for each 𝜆:

plot(cv.lasso)
The optimal value of 𝜆 is the one that minimizes the misclassification error. You can find it with:

optimal_lambda <- cv.lasso$lambda.min
optimal_lambda
This value of 𝜆 gives the smallest mean cross-validated error and is typically considered the optimal regularization strength for the model. The reason it's considered optimal is that it balances the trade-off between model complexity (number of features used) and model performance on unseen data (as estimated by cross-validation).