ee4001_2023T1_Q1_NA.pdf

[[IMAGE:48bcb6ba1b259b49_2_0]] 5. (3 points) Assume there are two Gaussian components in the GMM; suo, 11,00 and 01 define means and variances of these two components, 79 and (1 — 79) denote the mixture proportions of the two Gaussians (i.e. p(x) = oN (1,01) + (1 — 10)N (p12, 09). m * Yo . . @ * ° (a) (1 point) Draw on the figure the directions in which py and 1, will move during the next M-step. (b) (2 points) Will the estimate of mg increase or decrease on the next EM step? Explain your reasoning in one sentence. 6. (5 points) We saw two approaches to solve the sequence prediction problem: greedy and viterbi. Consider a weather sequence prediction problem, assuming first-order markov chain. Given that Sunny weather was observed on Day-0, compute the best: possible weather forcast sequence for the next three days using 1) greedy approach, 2) viterbi approach. Hint: For viterbi keep a track of path taken to calculate y4(B), where ya(B) denotes maximum probability of reaching state A at time step B. Today Sunny Cloudy Rainy Sunny [0.5 0.375 0,125 Yesterday Cloudy }0.25 0.125 0.625 Rainy 10,25 0.075 0.675 7. (3 points) We saw two approaches for vector quantization, namely: k-means & Linde-Buzo-Gray Algorithm (LBG). Explain in detail the clustering mechanism used in these two algorithms, highlighting differences in their approach. [[IMAGE:48bcb6ba1b259b49_4_2]]