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P c 1 s m a w 005 s m a w s 08 017 002 001 m 01 07

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Some of the values for the conditional probability table (CPT) are as follows. P ( C 1) : S M A W 0.15 0.6 0.2 0.05 S M A W S 0.8 0.17 0.02 0.01 M 0.1 0.7 0.19 0.01 A 0.02 0.05 0.7 0.23 W 0.2 0.01 0.04 0.7 Table 1: P ( C t +1 = j | C t = i ) for all t 1 (i:row, j:column) H R F S 0.4 0.3 0.3 M 0.5 0.45 0.05 A 0.3 0.4 0.3 W 0.0001 0.2499 0.75 Table 2: P ( O t = j | C t = i ) For inference, apply both sum–product and max–product algorithms to the following problems. Submit all of your codes (zipped as ’hw3BP.zip’) and report the results. (a) Compute the probability of ( S, M, A, W ) for each of all 20 observations (e.g., t, P ( C t = M | O 1 . . . O N )). Save the result of (4 × 20) probability matrix as ”gamma.txt”, and draw it into a figure as ”gamma.png” (x-axis: 20 time steps, y-axis: probability). Submit the ’gamma.txt’ and ’ ’gamma.png’. 4
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(b) Determine the most likely sequence of C 1 . . . C N that generated this observed sequence. 5
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