Question 4: Hidden Markov Models (overall 25 marks] (a) Given the three sets of sequence labels below of a 4-class problem (labels belong either to class 0, 1, 2, or 3), draw a state transition diagram. Include the probabilities of all transitions. Do not draw zero-probability transitions, [0 0 0 0 11111112222 3330000] [00 011122222233333 0 0 0] [0 0 0 1 1 1 2 2 1 1 1 2 2 23 333000] (8 marks) (b) For the data presented in question 4(a) above, give the prior probabilities of each state. (4 marks) (c) Draw a hidden Markov model for the data presented in question 4(a) above. Clearly indicate the direction of information flow, and information about observed and latent variables. (6 marks) (d) What are emission probabilities? Give an example of emission probabilities in the case of predicting the temporal phases onset, apex, offset, and neutral for facial expression recognition. (4 marks) (e) Explain how the Viterbi algorithm works. Illustrate your answer by giving pseudocode. (8 marks)