OUI (e) For some fixed setting of the parameters 0 and the observation y, plot various statistics of the Zi variables as a function of sampling iterations for the Gibbs sampler. Try various values of o2. How is convergence time affected? (f) Examine the data images. jpg shown on the course website. This shows 100 greyscale 4 x 4 images generated by randomly combining several features and adding some noise. Try to guess what these features are by inspecting the images. How many are there? Would you expect factor analysis to do a good job modeling these images? How about a mixture of Gaussians? Explain your reasoning. (g) Run your algorithms (EM based on Gibbs or mean field) on the data set generated by genimages . m. What features u do the algorithms find? (Rearrange them into 4 x 4 images). How do the Gibbs and mean field results differ? Explain any choices you make along the way and the rationale beyond them (e.g., how to set K, how to initialize parameters, latent states, and variational parameters)