[Solved] CSE417T Homework 2

1. Check out the files logisticreg.m and findtesterror.m from the SVN repository set up for this assignment. Also download the files clevelandtrain.csv and clevelandtest.csv from the Resources tab in Piazza. Note that these two files are not in the SVN repos and please do not add them there.

The source files are just function headers that need to be filled in. findtesterror 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 classification 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 vector to allow for a constant or bias term). logisticreg should encode a gradient descent algorithm for learning a logistic regression model. It should return a weight vector w and the training set error E_in (not the classification error, the negative log likelihood function) as 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.

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• Implement the functions in the two files. Remember to check in the final version ofyour code for these two files.
• Read more about the Cleveland dataset well be using here:_{uci.edu/ml/datasets/Heart+Disease} https://archive.
• Learn a logistic regression model on the data inabout the fact that the classes are 0/1 _{you should convert them to}csv1/ ₊₁(be carefulso that everything weve 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 E_in 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(learn about and use the binomial option, and check the label format). Compare theglmfit 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 deviationfor 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 E_in.

2. (15 points) LFD Exercise 4.5
3. (15 points) LFD Problem 4.8
4. (20 points) LFD Problem 4.25, parts (a) through (c) only