CSE555: Introduction to Pattern Recognition Midterm ... - CEDAR

We solve this equation and findwhich can be rewritten asThe final solution is then(1 − ˆP(wn∑i )) z ik = ˆP(wn∑i ) (1 − z ik )k=1k=1n∑z ik = ˆP(wn∑i ) z ik + n ˆP(w i ) − ˆP(wn∑i ) z ikk=1k=1k=1ˆP(w i ) = 1 n∑z iknk=1(c) (3pts) Interpret the meaning of your result in words.Answer:In this question, we apply the maximum-likelihood method to estimate the priorprobability. From the result in part (b), it can be observed that the estimate ofthe probability of category w i is merely the probability of obtaining its indicatoryvalue in the training data, just as we would expect.5. (20pts) Consider an HMM with an explicit absorber state w 0 and unique null visiblesymbol v 0 with the following transition probabilities a ij and symbol probabilities b jk(where the matrix indexes begin at 0):a ij =⎛⎜⎝1 0 00.2 0.3 0.50.4 0.5 0.1⎞⎟⎠ b jk =⎛⎜⎝1 0 00 0.7 0.30 0.4 0.6⎞⎟⎠(a) (7pts) Give a graph representation of this Hidden Markov Model.Answer:0.3ω0.210.3 0.7v2v110.50.5ω01v00.40.4v 1ω20.6v20.16