## Description

1. The LASSO and Boosting for Regression

(a) Download the Communities and Crime data1

from https://archive.ics.uci.

edu/ml/datasets/Communities+and+Crime. Use the first 1495 rows of data as

the training set and the rest as the test set.

(b) The data set has missing values. Use a data imputation technique to deal with

the missing values in the data set. The data description mentions some features

are nonpredictive. Ignore those features.

(c) Plot a correlation matrix for the features in the data set.

(d) Calculate the Coefficient of Variation CV for each feature, where CV =

s

m

, in

which s is sample standard deviation and m is sample mean..

(e) Pick b

√

128c features with highest CV , and make scatter plots and box plots for

them. Can you draw conclusions about significance of those features, just by the

scatter plots?

(f) Fit a linear model using least squares to the training set and report the test error.

(g) Fit a ridge regression model on the training set, with λ chosen by cross-validation.

Report the test error obtained.

(h) Fit a LASSO model on the training set, with λ chosen by cross-validation. Report

the test error obtained, along with a list of the variables selected by the model.

Repeat with standardized2

features. Report the test error for both cases and

compare them.

(i) Fit a PCR model on the training set, with M (the number of principal components) chosen by cross-validation. Report the test error obtained.

(j) In this section, we would like to fit a boosting tree to the data. As in classification

trees, one can use any type of regression at each node to build a multivariate

regression tree. Because the number of variables is large in this problem, one

can use L1-penalized regression at each node. Such a tree is called L1 penalized

gradient boosting tree. You can use XGBoost3

to fit the model tree. Determine

α (the regularization term) using cross-validation.

1Question you may encounter: I tried opening the dataset and download it but the file is not readable.

How to download the file? Just change .data to .csv. .

2

In this data set, features are already normalized.

3Some hints on installing XGBoost on Windows: http://www.picnet.com.au/blogs/guido/2016/09/

22/xgboost-windows-x64-binaries-for-download/.

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Homework 4 DSCI 552, Instructor: Mohammad Reza Rajati

2. Tree-Based Methods

(a) Download the APS Failure data from: https://archive.ics.uci.edu/ml/datasets/

APS+Failure+at+Scania+Trucks . The dataset contains a training set and a test

set. The training set contains 60,000 rows, of which 1,000 belong to the positive

class and 171 columns, of which one is the class column. All attributes are numeric.

(b) Data Preparation

This data set has missing values. When the number of data with missing values

is significant, discarding them is not a good idea. 4

i. Research what types of techniques are usually used for dealing with data with

missing values.5 Pick at least one of them and apply it to this data in the

next steps.6

ii. For each of the 170 features, calculate the coefficient of variation CV =

s

m

,

where s is sample standard deviation and m is sample mean.

iii. Plot a correlation matrix for your features using pandas or any other tool.

iv. Pick b

√

170c features with highest CV , and make scatter plots and box plots

for them, similar to those on p. 129 of ISLR. Can you draw conclusions about

significance of those features, just by the scatter plots? This does not mean

that you will only use those features in the following questions. We picked

them only for visualization.

v. Determine the number of positive and negative data. Is this data set imbalanced?

(c) Train a random forest to classify the data set. Do NOT compensate for class

imbalance in the data set. Calculate the confusion matrix, ROC, AUC, and

misclassification for training and test sets and report them (You may use pROC

package). Calculate Out of Bag error estimate for your random forset and compare

it to the test error.

(d) Research how class imbalance is addressed in random forests. Compensate for

class imbalance in your random forest and repeat 2c. Compare the results with

those of 2c.

(e) Model Trees

In the case of a univariate tree, only one input dimension is used at a tree split.

In a multivariate tree, or model tree, at a decision node all input dimensions can

be used and thus it is more general. In univariate classification trees, majority

polling is used at each node to determine the split of that node as the decision

rule. In model trees, a (linear) model that relies on all of the variables is used

4

In reality, wehn we have a model and we want to fill in missing values, we do not have access to training

data, so we only use the statistics of test data to fill in the missing values. For simplicity, in this exercise,

you first fill in the missing values and then split your data to training and test sets.

5They are called data imputation techniques.

6You are welcome to test more than one method.

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Homework 4 DSCI 552, Instructor: Mohammad Reza Rajati

to determine the split of that node (i.e. instead of using Xj > s as the decision

rule, one has P

j

βjXj > s. as the decision rule). Alternatively, in a regression

tree, instead of using average in the region associated with each node, a linear

regression model is used to determine the value associated with that node.

One of the methods that can be used at each node is Logistic Regression. One

can use scikit learn to call Weka7

to train Logistic Model Trees for classification.

Train Logistic Model Trees for the APS data set without compensation for class

imbalance. Use one of 5 fold, 10 fold, and leave-one-out cross validation methods

to estimate the error of your trained model and compare it with the test error.

Report the Confusion Matrix, ROC, and AUC for training and test sets.

(f) Use SMOTE (Synthetic Minority Over-sampling Technique) to pre-process your

data to compensate for class imbalance.8 Train a Logistic Model Tree using the

pre-processed data and repeat 2e. Do not forget that there is a right and a wrong

way of cross validation here. Compare the uncompensated case with SMOTE.

3. ISLR 6.8.3

4. ISLR, 6.8.5

5. ISLR 8.4.5

6. ISLR 9.7.3

7. Extra Practice: ISLR 5.4.2, 6.8.4, 8.4.4, 9.7.2

Appendix

Weka for Mac users:

1. Download JDK 9 from http://www.oracle.com/technetwork/java/javase/downloads/

index.html

2. Add environment variables in Terminal using : vi~/.bash_profile

(a) export JAVA_HOME=/Library/Java/JavaVirtualMachines/jdk-9.0.4.jdk/Contents/

Home

(b) export PATH=$JAVA_HOME/bin:$PATH

3. Restart Terminal

4. Get brew (package installer for Mac, if you don’t have it) and install python (not

necessary)

7http://fracpete.github.io/python-weka-wrapper/install.html. may help.

8

If you did not start doing this homework on time, downsample the common class to 6,000 so that you

have 12,000 data points after applying SMOTE. Remember that the purpose of this homework is to apply

SMOTE to the whole training set, not the downsampled dataset.

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Homework 4 DSCI 552, Instructor: Mohammad Reza Rajati

5. brew install pkg-config

6. brew install graphviz

7. pip install javabridge

8. pip install python-weka-wrapper

And you should be able to use WEKA in your Jupyter Notebooks.

4