Problem 1. Implement logistic regression with both the “accuracy” and the “binary cross entropy” objective functions, and study how the results and the performance of the algorithm differ.
Problem 2. Implement ridge regression with various values of the regularization parameter, and also compare with using pseudo-inverse with various values of the cutoff parameter. Try them both on the data set where the input variable is a vector of dimension two, where the both entries (and the output variables) are equal to i + N(0.1, 1), where i goes from 0 to 100000.
Problem 3. (a more realistic version of problem 2). Use the inputs the day to day changes of the prices of the four stock indices (DJIA, S&P 500, Russell 2000, and Nasdaq 100) and as output the change in price of MSFT. Have your analysis run over the period of the last 20 years. Figuring out where to get the data is part of the project.
Problem 4. Do variants of problem 3 for different one-year-long periods in history to see if the statistics change over time.