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Homework 4 CSCE 633

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Homework 4 CSCE 633

Instructions for homework submission
Please submit on eCampus a single pdf file containing your solutions.
a) Please write a brief report and include your code right after each answer.
b) For each answer, please explain your thought process, results, and observations. Please do
not just include your code without justification.
c) Create a single pdf and submit it on eCampus. Please do not submit .zip files or colab
notebooks.
d) The maximum grade for this homework is 6 points (out of 100 total for the class).
Question: Decision Tree and Random Forest
Classifying benign vs malignant tumors: We would like to classify if a tumor is benign or malign based on its attributes. We use data from the Breast Cancer Wisconsin Data
Set of the UCI Machine Learning Repository: https://archive.ics.uci.edu/ml/datasets/
breast+cancer+wisconsin+(original).
Inside “Homework 4” folder on Piazza you can find one file containing the train data (“hw4
train.csv”) and test data (“hw4 test.csv”) for our experiments. The rows of these files refer to
the data samples, while the columns denote the features (columns 1-9) and the outcome variable
(column 10), as described bellow:
1. Clump Thickness: discrete values {1, 10}
2. Uniformity of Cell Size: discrete values {1, 10}
3. Uniformity of Cell Shape: discrete values {1, 10}
4. Marginal Adhesion: discrete values {1, 10}
5. Single Epithelial Cell Size: discrete values {1, 10}
6. Bare Nuclei: discrete values {1, 10}
7. Bland Chromatin: discrete values {1, 10}
8. Normal Nucleoli: discrete values {1, 10}
9. Mitoses: discrete values {1, 10}
10. Class: 2 for benign, 4 for malignant (this is the outcome variable)
(1) (1 point) Data exploration: Using the training data, plot the histograms of the class
outcome and each feature (i.e., 10 histograms total). Compute the number of samples belonging
to the benign and the number of samples belonging to the malignant case.
(2) (1 point) Conditional entropy: Implement a function that computes the conditional
entropy of each feature, conditioned on the class outcome. Using the training data, compute
the conditional entropies for each feature (i.e., 9 values total). Which features are the most
discriminative of the outcome?
1
Hint: For implementing the conditional entropy, please follow the example that we discussed in
class.
(3) (2 points) Decision tree classification: Use a decision tree classifier to classify between benign and malignant tumor based on the features provided. Identify the optimal hyperparameters (e.g., tree depth) using hyper-parameter tuning through a 5-fold cross-validation
on the training set. Report the classification accuracy for all hyper-parameters from the crossvalidation process on the training set, as well as the classification accuracy on the test set using
the best hyper-parameter from the cross-validation.
Note: You can use any available library for the decision tree and the cross-validation.
(4) (2 points) Random forest tree classification: Repeat the same task as in question (3)
using a random forest classifier. Experiment with the optimal tree depth and number of trees.
Compare and contrast the performance of the decision tree with the random forest classifier.
Note: You can use any available library for the random forest and the cross-validation.
2

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