You're interested in knowing whether you would be (S)atisfied with your choice of snacks, and so...

    

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You're interested in knowing whether you would be (S)atisfied with your choice of snacks, and so you decide to make the prediction using probabilistic inference over a model with the following variables: S, whether or not you will be Satisfied. H, whether or not you will be Hungry. T, whether or not you will be Thirsty. P, whether or not you will have Pizza. B, whether or not you will have Boba. You model this problem with the following Bayes Net: P H S B T Pr(H) +h 0.7 -h 0.3 Pr(T) +t 0.6 -t 0.4 Pr(PH) +p+h 0.8 -h 0.5 +h 0.2 -h 0.5 +p -P -P Pr(BH,T) Pr(SIP, B) +p+b 0.9 +s +p-b 0.4 +b +h +t 0.4 +b +h -t 0.2 +b -h +t +b-h +8 0.9 +s -P +6 0.7 0.5 +$ -P -b 0.1 -b +h +t 0.6 -8 +p+b 0.1 -b +h +p -b 0.6 -t 0.8 -b -h +t 0.1 -P +b 0.3 -b -h -t 0.5 -8 -P -b 0.9 -8 -S (a) You do not know which snack(s) you are going for, but you know you are both hungry, thirsty, and definitely getting Pizza. According to your model, what is the probability that you will be satisfied? (b) After some thinking, you decided on a choice of snack(s). Given that you are satisfied with your choice of snack(s), write out the variable elimination steps you would take to compute the probability that you actually had boba, that is, P(+b+s). (You do not have to plug in the values from the tables). (1) Which factors do we start with? (II) Run variable elimination to eliminate three variables. For each one, determine the variable to be eliminated, compute the expression for the new factor you generate (in terms of the other factors you have), and then show the new list of factors after the elimination. (III) After eliminating three variables, you should be able to compute P(+b| +s). Write the expression for P(+b| +s) in terms of the factors you have left. You're interested in knowing whether you would be (S)atisfied with your choice of snacks, and so you decide to make the prediction using probabilistic inference over a model with the following variables: S, whether or not you will be Satisfied. H, whether or not you will be Hungry. T, whether or not you will be Thirsty. P, whether or not you will have Pizza. B, whether or not you will have Boba. You model this problem with the following Bayes Net: P H S B T Pr(H) +h 0.7 -h 0.3 Pr(T) +t 0.6 -t 0.4 Pr(PH) +p+h 0.8 -h 0.5 +h 0.2 -h 0.5 +p -P -P Pr(BH,T) Pr(SIP, B) +p+b 0.9 +s +p-b 0.4 +b +h +t 0.4 +b +h -t 0.2 +b -h +t +b-h +8 0.9 +s -P +6 0.7 0.5 +$ -P -b 0.1 -b +h +t 0.6 -8 +p+b 0.1 -b +h +p -b 0.6 -t 0.8 -b -h +t 0.1 -P +b 0.3 -b -h -t 0.5 -8 -P -b 0.9 -8 -S (a) You do not know which snack(s) you are going for, but you know you are both hungry, thirsty, and definitely getting Pizza. According to your model, what is the probability that you will be satisfied? (b) After some thinking, you decided on a choice of snack(s). Given that you are satisfied with your choice of snack(s), write out the variable elimination steps you would take to compute the probability that you actually had boba, that is, P(+b+s). (You do not have to plug in the values from the tables). (1) Which factors do we start with? (II) Run variable elimination to eliminate three variables. For each one, determine the variable to be eliminated, compute the expression for the new factor you generate (in terms of the other factors you have), and then show the new list of factors after the elimination. (III) After eliminating three variables, you should be able to compute P(+b| +s). Write the expression for P(+b| +s) in terms of the factors you have left.