Variable Selection for Sparse Logistic Regression Assignment

Assignment Task

1. Implement the FSA variable selection method for linear models and binary classification with the logistic loss, as described in the slides. Use the parameters s =0.001,μ = 100,Niter = 300. Take special care to normalize each column of the X matrix to have zero mean and variance 1 and to use the same mean and standard deviation that you used for normalizing the train set also for normalizing the test set.

a. Using the Gisette data, train a FSA classifier on the training set, starting with β(0)= 0 to select k ∈ {10,30,100,300,500} features. Plot the training loss vs iteration number for k = 300. Report in a table the misclassification errors on the training and test set for the models obtained for all these k. Plot the misclassification error on the training and test set vs k. Also plot the train and test ROC curves of the obtained model with 300 features. 

b. Repeat point a) on the dexter dataset.

c. Repeat point a) on the Madelon dataset.

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