STAT 432 Homework 07

---

For this homework, you may only use the following packages:

# general
library(MASS)
library(caret)
library(tidyverse)
library(knitr)
library(kableExtra)
library(mlbench)

# specific
library(ISLR)
library(ellipse)
library(randomForest)
library(gbm)
library(glmnet)
library(rpart)
library(rpart.plot)

---

Exercise 1 (Classifying Leukemia)

[7 points] For this question we will use the data in leukemia.csv which originates from Golub et al. 1999.

The response variable class is a categorical variable. There are two possible responses: ALL (acute myeloid leukemia) and AML (acute lymphoblastic leukemia), both types of leukemia. We will use the many feature variables, which are expression levels of genes, to predict these classes.

Note that, this dataset is rather large and you may have difficultly loading it using the “Import Dataset” feature in RStudio. Instead place the file in the same folder as your .Rmd file and run the following command. (Which you should be doing anyway.) Again, since this dataset is large, use 5-fold cross-validation when needed.

leukemia = read_csv("leukemia.csv", progress = FALSE)

For use with the glmnet package, it will be useful to create a factor response variable y and a feature matrix X as seen below. We won’t test-train split the data since there are so few observations.

y = as.factor(leukemia$class)
X = as.matrix(leukemia[, -1])

Do the following:

• Set a seed equal to your UIN.
• Fit the full path of a logistic regression with both a lasso penalty and a ridge penalty. (Don’t use cross-validation. Also let glmnet choose the \(\lambda\) values.) Create side-by-side plots that shows the features entering (or leaving) the models.
• Use cross-validation to tune an logistic regression with a lasso penalty. Again, let glmnet choose the \(\lambda\) values. Store both the \(\lambda\) that minimizes the deviance, as well as the \(\lambda\) that has a deviance within one standard error. Create a plot of the deviances for each value of \(\lambda\) considered. Use these two \(\lambda\) values to create a grid for use with train() in caret. Use train() to get cross-validated classification accuracy for these two values of \(\lambda\). Store these values.
• Use cross-validation to tune an logistic regression with a ridge penalty. Again, let glmnet choose the \(\lambda\) values. Store both the \(\lambda\) that minimizes the deviance, as well as the \(\lambda\) that has a deviance within one standard error. Create a plot of the deviances for each value of \(\lambda\) considered. Use these two \(\lambda\) values to create a grid for use with train() in caret. Use train() to get cross-validated classification accuracy for these two values of \(\lambda\). Store these values.
• Use cross-validation to tune \(k\)-nearest neighbors using train() in caret. Do not specify a grid of \(k\) values to try, let caret do so automatically. (It will use 5, 7, 9.) Store the cross-validated accuracy for each. Scale the predictors.
• Summarize these seven models in a table. (Two lasso, two ridge, three knn.) For each report the cross-validated accuracy and the standard deviation of the accuracy.

Solution:

uin = 123456789
set.seed(uin)
cv_5 = trainControl(method = "cv", number = 5)

fit_lasso = glmnet(X, y, family = "binomial", alpha = 1)
fit_ridge = glmnet(X, y, family = "binomial", alpha = 0)

par(mfrow = c(1, 2))
plot(fit_lasso, xvar = "lambda", main = "Lasso")
plot(fit_ridge, xvar = "lambda", main = "Ridge")