# Homework #3 SOlution

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## Description

Notes:

Please check the submission instructions for Gradescope provided on the course website. You must follow those instructions exactly.

Please download the following files (two stub Matlab files and two data files) for Problem 1. http://classes.cec.wustl.edu/˜cse417t/hw3/hw3_files.html

Complete and submit the Matlab files. In addition, you need to separately submit a write-up with written solutions for all problems (including the results and reports for programming problems) to Gradescope. Your score will be based on the report. The code you submit is only used for checking correctness and for running plagiarism checkers. Results included in the code submission will not be graded.

Homework is due by 11:59 PM on the due date. Remember that you may not use more than 2 late days on any one homework, and you only have a budget of 5 in total.

Please keep in mind the collaboration policy as specified in the course syllabus. If you dis-cuss questions with others you must write their names on your submission, and if you use any outside resources you must reference them. Do not look at each others’ writeups, in-cluding code.

Please do not directly post your answers on Piazza even if you think they might be wrong. Please try to frame the question such that you dont give the answers away. If there is specific information you want to ask about your answers, try the office hours or private posts on Piazza.

There are 4 problems on 2 pages in this homework.

Keep in mind that problems and exercises are distinct in LFD.

Problems:

1. (60 points) The two stub Matlab files are just function headers that need to be filled in. find test error should encode a function that, given as inputs a weight vector w, a data matrix X and a vector of true labels y (in the formats defined in the header), returns the clas-sification error of w on the data (assuming that the classifier applies a threshold at 0 to the dot product of w and a feature vector x (augmented with a 1 in the first position in the vec-tor to allow for a constant or bias term). logistic reg should encode a gradient descent algorithm for learning a logistic regression model. It should return a weight vector w and the training set error Ein (not the classification error, the negative log likelihood function) as

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defined in class. Use a learning rate = 10 5 and automatically terminate the algorithm if the magnitude of each term in the gradient is below 10 3 at any step.

Implement the functions in the two files. Remember to submit your code to Grade-scope.

Read more about the “Cleveland” dataset we’ll be using here: https://archive. ics.uci.edu/ml/datasets/Heart+Disease

Learn a logistic regression model on the data in clevelandtrain.csv (be careful about the fact that the classes are 0=1 – you should convert them to 1= + 1 so that everything we’ve done in class is still valid). Apply the model to classify the data (using a probability of 0:5 as the threshold) in clevelandtest.csv. In your writeup, report Ein as well as the classification error on both the training and test data when using three different bounds on the maximum number of iterations: ten thousand, one hundred thousand, and one million. What can you say about the generalization properties of the model?

Now train and test a logistic regression model using the inbuilt matlab function glmfit (learn about and use the “binomial” option, and check the label format). Compare the results with the best ones you achieved and also compare the time taken to achieve the results.

Now scale the features by subtracting the mean and dividing by the standard deviation for each of the features in advance of calling the learning algorithm (you may find the matlab function zscore useful). Experiment with the learning rate (you may want to start by trying different orders of magnitude), this time using a tolerance (how close to zero you need each element of the gradient to be in order to terminate) of 10 6. Report the results in terms of number of iterations until the algorithm terminates, and also the final Ein.

1. (15 points) LFD Problem 3.19

1. (10 points) LFD Exercise 4.5 (Not Problem 4.5)

1. (15 points) LFD Problem 4.8

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