本次美国CS代写主要是机器学习的基础知识包括决策树等

CSCI 5521: Machine Learning Fundamentals (Spring 2021)

Homework 3

(Due Tue, Mar. 30, 11:59 PM central)

1. (15 points) Consider a binary classification problem with two possible choices (Price and WaitEstimate) for the root of a decision tree for the restaurant dataset as shown in the figure. The green (top row) and red circles (bottom row) refer to the data points from the two classes where the green (top row) circles belong to class 0 and red (bottom row) belong to class 1.

Calculate the information gain for the attributes ‘Price’ and ‘WaitEstimate’ showing all steps. Based on the calculated information gain, which attribute will you use as the root of the decision tree (Price or WaitEstimate)? Justify your answer by describing what the information gain numbers mean.

Programming assignment:

2. (85 points) In this problem, we will use the Digits dataset to classify ‘3’ vs ‘8’. Your task is to build three classifiers: (a) bagging, (b) random forests, and (c) adaboost. You must implement each classifier, from scratch, using only the provided code and functions specified in this problem description and additional instructions below.

(a) (25 points) Write code for class MyBagging in file MyBagging.py with two key functions: MyBagging.fit(self, X, r) and MyBagging.predict(self, X).

For the class, the init (self, num trees, max depth) function takes as input num trees which is the number of tree classifiers in the ensemble (must be an integer ≥ 1), and max depth which is the maximum depth of the trees.

For fit(self, X, r), the inputs (X, r) are the feature matrix and class labels respec- tively. The fit function will construct num trees number of bootstrap datasets and learn a distinct decision tree on each bootstrap dataset. To learn a decision tree, you must use the class DecisionTreeClassifier from scikit-learn. You must set the decision tree hyperparameters as: criterion=‘entropy’, and random state = 0.

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For predict(self, X), the input X is the feature matrix corresponding to the validation set and the output should a list of length equal to num trees. Each element in the list should be an array of length equal to the number of data points in the validation set. The array should contain the predicted labels for each data point in the validation set using the ensemble of trees built up to that point. For example, the predictions in the array in the first element of the output list should be made only using the first decision tree constructed in the ensemble. The predictions in the array in the second element of the output list should be made using the first two decision trees constructed in the ensemble. The predictions in the array in the t-th element of the output list should be made using the first t decision trees constructed in the ensemble. The predictions in the array in the last element of the output list should be made using all decision trees in the ensemble. By constructing the output list in this way, we can use the hw3q2.py script to plot the mean error rate as we increase the number of trees in the ensemble.

(b) (25 points) Write code for class MyRandomForest in file MyRandomForest.py with two key functions: MyRandomForest.fit(self,X,r) and MyRandomForest.predict(self,X).

For the class, the init (self, num features, num trees, max depth) function takes as input num features which is the number of random features to choose at each split in the decision tree (the variable m from the lecture notes, and must be 1 ≤ num features ≤ d), num trees which is the number of tree classifiers in the ensemble (must be an integer ≥ 1), and max depth which is the maximum depth of the trees.

For fit(self, X, r), the inputs (X, r) are the feature matrix and class labels respec- tively. The fit function will construct num trees number of bootstrap datasets and learn a distinct decision tree on each bootstrap dataset. To learn a decision tree, you must use the class DecisionTreeClassifier from scikit-learn with the same parameters as specified in MyBagging.

For predict(self, X), the input X is the feature matrix corresponding to the validation set and the output should a list of length equal to num trees where each element is an array of predicted labels for each point in the validation set (constructed in the same way as in MyBagging).

(c) (35 points) Write code for class MyAdaboost in file MyAdaboost.py with two key func- tions: MyAdaboost.fit(self, X, r) and MyAdaboost.predict(self, X).

For the class, the init (self,num iters,max depth) function takes as input num iters which is the number of tree classifiers (i.e., number of iterations – the variable T from the lecture notes) in the ensemble and max depth which is the maximum depth of the trees.

For fit(self,X,r), the inputs are the feature matrix and the class labels respectively. The fit function will construct the weight distribution wt in each iteration t and learn a distinct decision tree using the dataset X and wt. It is recommended to learn a tree using wt by sampling with replacement from X following distribution wt to create a temporary dataset which then is given to the decision tree algorithm. (Consider using the random.choices() function.)

The fit function will also compute the weighted error rates εt and classifier weights αt in 2

each iteration t. To learn a decision tree, you must use the class DecisionTreeClassifier from scikit-learn with the same parameters as specified in MyBagging.

For predict(self, X), the input X is the feature matrix corresponding to the validation set and the output should a list of length equal to num iters where each element is an array of predicted labels for each point in the validation set (constructed in the same way as in MyBagging).

We will compare the performance of these three classifiers (note the output from your code and reported in your solution pdf must be in this order):

- (i) MyBagging with num trees = 100 using DecisionTreeClassifier with max depth = 1,
- (ii) MyBagging with num trees = 100 using DecisionTreeClassifier with max depth = None,
- (iii) MyRandomForest with num features=1, num trees=100 using MyDecisionTree with max depth=1,
- (iv) MyRandomForest with num features = sqrt(d), num trees = 100 using DecisionTreeClassifier
with max depth = 1,

- (v) MyRandomForest with num features = 1, num trees = 100 using DecisionTreeClassifier
with max depth = None,

- (vi) MyRandomForest with num features = sqrt(d), num trees = 100 using DecisionTreeClassifier
with max depth = None,

- (vii) MyAdaboost with num trees = 100 using DecisionTreeClassifier with max depth = 1,
- (viii) MyAdaboost with num trees = 100 using DecisionTreeClassifier with max depth = None,

applied to the Digits dataset. Using the code provided for hw3q2.py and my cross val() with 5-fold cross-validation, report the error rates in each fold as well as the mean and standard deviation of error rates across folds for each of the above 8 settings.

You will have to submit (a) code and (b) summary of results:

(a) Code: You will have to submit code for MyBagging, MyRandomForest, and MyAdaboost. We provide template code for the following classes and functions. Please read the com- ments in the code carefully especially in the predict() functions.

class MyBagging:

def init (self, num trees, max depth): def fit(self, X, r):

def predict(self, X):

class MyRandomForest:

def init (self, num features, num trees, max depth):

def fit(self, X, r):

def predict(self, X):

class MyAdaboost:

def init (self, num iters, max depth):

def fit(self, X, r): def predict(self, X):

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Your classes should not inherit any base class in sklearn other than DecisionTreeClas- sifier. Again, the three functions you must implement in each class are are init , fit, and predict.

The wrapper script hw3q2.py is used to prepare the dataset, initialize class objects, make calls to my cross val(method,X,r,k) to generate the error rate results (here k is the number of folds), and print the results. You must use this wrapper script or no credit will be given.

(b) Summary of results: To generate the results, run the hw3q2.py script. For each method, report the validation set error rates for each of the k = 5 folds, the mean error rate over the k folds, and the standard deviation of the error rates over the k folds. Make a table to present the results for each method (8 tables in total). Each column of the table represents a fold, and add two columns at the end to show the overall mean error rate and standard deviation over the k folds (see below for an example). Also, include in your report the figure hw3q2.png which is generated after running hw3q2.py.

Error rates for MyBagging with num trees = 100, num depth = 1 Fold1 Fold2 Fold3 Fold4 Fold5 Mean SD

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Additional instructions: Code can only be written in Python 3.6+; no other programming languages will be accepted. One should be able to execute all programs from the Python command prompt or terminal. Please specify instructions on how to run your program in the README file.

Each function must take the inputs in the order specified in the problem and display the textual output via the terminal and plots/figures should be included in the report.

For each part, you can submit additional files/functions as needed. In your code, you can only use machine learning libraries such as those available from scikit-learn as specified in the problem description. You may use libraries for basic matrix computations and plotting such as numpy, pandas, and matplotlib. Put comments in your code so that one can follow the key parts and steps in your code.

Your code must be runnable on a CSE lab machine (e.g., csel-kh1260-01.cselabs.umn.edu). One option is to SSH into a machine. Learn about SSH at these links: https://cseit.umn.edu/ knowledge-help/learn-about-ssh, https://cseit.umn.edu/knowledge-help/choose-ssh-tool, and https://cseit.umn.edu/knowledge-help/remote-linux-applications-over-ssh.

Instructions

Follow the rules strictly. If we cannot run your code, you will not get any credit. Things to submit

1. hw3.pdf: A document which contains the solution to Problems 1 and 2 including the summary of results for Problem 2. This document must be in PDF format (no word, photo, etc. is accepted). If you submit a scanned copy of a hand-written document, make sure the copy is clearly readable, otherwise no credit may be given. Do not include

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the PDF file within the ZIP file. Rather, the PDF document should be submitted as a separate document.

- PythoncodeforProblem2(mustincludetherequiredMyBagging.py,MyRandomForest.py, and MyAdaboost.py files).
- README.txt: README file that contains your name, student ID, email, instructions on how to run your code, any assumptions you are making, and any other necessary details.
- Any other files, except the data, which are necessary for your code (such as package dependencies like a requirements.txt or yml file).

Homework Policy. (1) You are encouraged to collaborate with your classmates on homework problems, but each person must write up the final solutions individually. You need to list in the README.txt which problems were a collaborative effort and with whom. (2) Regarding online resources, you should not:

Google around for solutions to homework problems,

Ask for help on online,

Look up things/post on sites like Quora, StackExchange, etc.

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