Question: (i) Derive the EM algorithm for a multivariate normal mixture model with H components. That is - derive the E and M steps for the

(i) Derive the EM algorithm for a multivariate

(i) Derive the EM algorithm for a multivariate normal mixture model with H components. That is - derive the E and M steps for the update equations for the means, covariance matrices and proportion parameters, as given in the lecture notes. To do this you will likely need basic Lagrange multiplier optimisation (for the mixing proportions) and the Matrix Cookbook or similar. [6 marks]

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