INSTRUCTIONS: To run the program and get all output (from command line and in results folder), simply run: $ python3 main.py

Task 1

• Plot training set MSE and test set MSE (BOTH!) against gamma
• Compare these values with the true MSE of the true functions
• Why cannot use training set results to select gamma
• How gamma affects error on the test set
• How to explain these effects

Task 2

• Pick 3 gamma values: too small, just right, too large
• Find the learning curve on the 1000-100 dataset ONLY!
• Vary the training size between 10 and 800 samples (not the whole training set)
• How does test set MSE depend on both gamma and training size

Task 3

• Implement the iterative method to find alpha and beta
• Apply to all 5 datasets
• Show how this compares to the results from task 1 in terms of both lambda and mse
• How quality depends on number of examples and features? (This is done by looking at the first 3 datasets)

Task 4

• For d = 1: 10, run model selection to choose alpha, beta and find log evidence
• Calculate MSE on test set using MAP for prediction
• Also run non-regularized on the same data set and calculate MSE (augmented dataset)
• The log evidence is done on the train data set?
• Plot log evidence and 2 MSE values over d
• Should we choose alpha, beta and d based on log evidence?

Task 1 output optimal lambda: 8 MSE: 4.15967850948 optimal lambda: 22 MSE: 5.07829980059 optimal lambda: 27 MSE: 4.31557063032 optimal lambda: 75 MSE: 0.389023387713 optimal lambda: 2 MSE: 0.625308842305