1.(20 pts) (Exercise 14.21) Consider the query P(Rain | Sprinkler = true, WetGrass = true) in...
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1.(20 pts) (Exercise 14.21) Consider the query P(Rain | Sprinkler = true, WetGrass = true) in the figure below and how Gibbs sampling can answer it. Sprinkler CP(Sc) .10 50 P(C=.5) Cloudy WetGrass SRP(Ws.r) 99 .90 tt ft .90 .00 Rain T f P(RC) 80 20 (a) (2 pts) How many states does the Markov chain for this query have? (b) (10 pts) Calculate the transition matrix Q containing the kernel k(y →y') for every directed edge from, say, a state y to another state y' or itself (in the case y = y'), in the Markov chain. Label the rows and columns of the matrix by the states such that an entry in the matrix corresponds to the probability of a transition from the state given by the row label to the state given by the column label. (c) (2 pts) What does Q², the square of the transition matrix, represent? (d) (3 pts) What about Q" as n → ∞? (e) (3 pts) Explain how to do probabilistic inference in a Bayesian network, assuming that Q" is available. Is this a practical way to do inference? 1.(20 pts) (Exercise 14.21) Consider the query P(Rain | Sprinkler = true, WetGrass = true) in the figure below and how Gibbs sampling can answer it. Sprinkler CP(Sc) .10 50 P(C=.5) Cloudy WetGrass SRP(Ws.r) 99 .90 tt ft .90 .00 Rain T f P(RC) 80 20 (a) (2 pts) How many states does the Markov chain for this query have? (b) (10 pts) Calculate the transition matrix Q containing the kernel k(y →y') for every directed edge from, say, a state y to another state y' or itself (in the case y = y'), in the Markov chain. Label the rows and columns of the matrix by the states such that an entry in the matrix corresponds to the probability of a transition from the state given by the row label to the state given by the column label. (c) (2 pts) What does Q², the square of the transition matrix, represent? (d) (3 pts) What about Q" as n → ∞? (e) (3 pts) Explain how to do probabilistic inference in a Bayesian network, assuming that Q" is available. Is this a practical way to do inference?
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a Number of States To determine the number of states in the Markov chain for this query you need to consider the possible combinations of values for t... View the full answer
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Artificial Intelligence A Modern Approach
ISBN: 978-0137903955
2nd Edition
Authors: Stuart J. Russell and Peter Norvig
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