This assignment is about fitting mixtures of axis-aligned Gaussians to
two-dimensional data. Copy the files below into your directory:

http://www.cs.toronto.edu/~hinton/csc321/matlab/mogem.m
http://www.cs.toronto.edu/~hinton/csc321/matlab/moginit.m
http://www.cs.toronto.edu/~hinton/csc321/matlab/plotellipse.m
http://www.cs.toronto.edu/~hinton/csc321/matlab/showmog.m


PART 1 (5 points) 

Run moginit to create training and validation datasets from 12 random
Gaussians.  Then use the function mogem to fit various numbers of
Gaussians to the training data.  Using performance on the validation
data, determine the optimal number of Gaussians to fit to the training
data. Present your results as a graph that plots both the validation
density and the training density as a function of the number of
Gaussians. Include a brief statement of what you think the graph
shows. Also include a brief statement about the effects of changing
the initial standard deviation used in mogem.

Please do not change the random seeds in moginit.m (this will produce
different data). You can do this later if you want to just play around
and get a feel for how the algorithm behaves.


PART 3 (3 points)

Change moginit.m to use only 4 cases per Gaussian and repeat the
experiment above (without changing the random seeds). Present your
results as a graph and include a brief statement of what you think the
graph shows and why it differs from the graph in PART 1.