Please see the homework policy document for detailed instructions and some grading notes. Failure to follow instructions will result in point reductions.
“Statisticians, like artists, have the bad habit of falling in love with their models.”
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)If you feel additional general packages would be useful for future homework, please pass these along to the instructor.
[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:
glmnet choose the \(\lambda\) values.) Create side-by-side plots that shows the features entering (or leaving) the models.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.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.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.[5 points] For this exercise, we will use the College data from the ISLR package. Familiarize yourself with this dataset before performing analyses. We will attempt to predict the Outstate variable.
Test-train split the data using this code.
set.seed(42)
index = createDataPartition(College$Outstate, p = 0.75, list = FALSE)
college_trn = College[index, ]
college_tst = College[-index, ]Train a total of six models using five-fold cross validation.
tuneLength of 10.tuneLength of 10.Before beginning, set a seed equal to your UIN.
uin = 123456789
set.seed(uin)[5 points] For this exercise we will create data via simulation, then assess how well certain methods perform. Use the code below to create a train and test dataset.
set.seed(42)
sim_trn = mlbench.spirals(n = 2500, cycles = 1.5, sd = 0.125)
sim_trn = data.frame(sim_trn$x, class = as.factor(sim_trn$classes))
sim_tst = mlbench.spirals(n = 10000, cycles = 1.5, sd = 0.125)
sim_tst = data.frame(sim_tst$x, class = as.factor(sim_tst$classes))The training data is plotted below, with colors indicating the class variable, which is the response.