# More formally if we let c i denote the season on the

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day, the weather that day is independent of all other variables. More formally, if we let C i denote the season on the i th day (taking values S,A,W) and O i denote the observed weather pattern(one of H,R,F); we have j < i - 1 C i C j | C i - 1 and X, O i X | C i where X is any random variable other than C i , O i . 1. Draw a graphical model over C 1 . . . C N , O 1 . . . O N that satisfies the conditional independencies listed above. 2. Implement sum-product and max-product algorithms in MATLAB, for this graphical model. In order to fully specify the graphical model, you will need to fill the values for the CPT. Some of these are 3

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listed in params.txt Assume a uniform distribution for any additional CPTs that you think you need to fully specify your graphical model (Hint: You will need one additional CPT). 3. Cecilia has made 20 observation of the weather over the last few months(ie O 1 . . . O N ). This data is in weather.txt. (a) Apply inference, to compute the most likely season for each of these days and submit the output in a textfile called hw1-a.txt (b) Apply inference to determine the most likely sequence of C 1 . . . C N that generated this observed sequence. Submit your output in a textfile called hw1-b.txt (c) Cecilia made the last observation today. Who do you think was correct? What is the probability that it is currently winter in Markovford? Submit your code and a readme describing briefly what each file does, along with the output listed above. 4
• Fall '07
• CarlosGustin
• Probability theory, probability density function, Cecilia, Bayesian network, graphical model, Belief propagation

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