Exercises, II part Forward Chaining: 12 Jul 2012 Exercises, II - PDF document

Exercises, II part Exercises, II part Forward Chaining: 12 Jul 2012 Exercises, II part Consider the following set of clauses in propositional logic: J = ⇒ Q A ∧ I = ⇒ J E ∧ F = ⇒ I B = ⇒ F A ∧ B = ⇒ E A B 1 Show and execution of the forward chaining algorithm on this set of clauses for proving Q (show the and-or graph and the evolution of the count table). 2 What happens if we replace the first clause of the knowledge base J = ⇒ Q with J ∧ G = ⇒ Q (and nothing else changes in the knowledge base)?

Forward Chaining: 27 Sep 2012 Exercises, II part Consider the following set of clauses in propositional logic: H ∧ S = ⇒ Q M ∧ S = ⇒ H H ∧ A = ⇒ M M ∧ B = ⇒ S A ∧ B = ⇒ M A B 1 Show an execution of the forward chaining algorithm on this set of clauses for proving Q (show the and-or graph and the evolution of the count table). 2 Briefly comment on the complexity and completeness of the forward chaining approach. Inference: 12 Jul 2012 Exercises, II Consider the following Joint Probability Table for the three binary ran- part dom variables A , B , C . P ( A , B , C ) A B C 0.108 T T T 0.012 T T F 0.072 T F T 0.008 T F F 0.016 F T T 0.064 F T F 0.144 F F T 0.576 F T F Compute the following queries: 1 P(C|A=T,B=T) 2 P(C|A=T)

BN: 13 Feb. 2017 Exercises, II part Consider the Bayesian Network in the Figure. Answer the following questions: State whether 1 P(A|B,C) = P(A|B,C,D). Motivate your answer. State whether 2 P(A|C) = P(A|B,C,D). Motivate your answer. State how many numbers we 3 need to represent the joint distribution for this network assuming variables are all boolean. Motivate your answer. BN: 16 Giu. 2016 Exercises, II Consider the Bayesian Network in part Figure, where every variable is by- nary. Answer the following ques- tions: Is it true 1 that P(B|A) = P(B|A,C) ? Motivate your answer. Write down 2 the equation to compute the query P(D|A=true,C=true) using the CPT associated with the network. How many independent 3 numbers must be stored to answer all the possible queries for this Bayesian Network ?

BN: 21 Sep. 2016 Exercises, II part Consider the Bayesian Network in Figure, where every variable is by- nary. Answer the following ques- tions: State how many 1 parameters must be provided to compute the joint probability table of this BN. Assume the CPT 2 that defines P(E|B,C,D) is specified with a noisy-or, state how many parameters must be provided to compute the joint probability table of this BN. State whether P(D|C,E) = 3 P(D|A,B,C,E). Motivate your answer. Minimax: 16 Giu. 2016 Exercises, II part Consider the min-max tree in Figure. Is it possible to provide a set of values to replace the question marks so that an Aplha-Beta pruning algorithm would perform the specified cuts ? If so provide such values otherwise motivate your answer.

Minimax: 26 Sep 2013 Exercises, II part Consider the min-max tree in the Figure. Show a trace of the execution of an Aplha-Beta pruning algorithm, indicating what will be the first move selected by the max player and which cuts are performed by the algorithm. DPOP: 22 Jun. 2015 Exercises, II part Consider the following cost network: Variables, binary X = { x 1 , x 2 , x 3 , x 4 , x 5 } . Constraints C h = { } and C s = { F 12 ( x 1 , x 2 ) , F 13 ( x 1 , x 3 ) , F 15 ( x 1 , x 5 ) , F 23 ( x 2 , x 3 ) , F 34 ( x 3 , x 4 ) , F 45 ( x 4 , x 5 ) } . Consider the DPOP algorithm: show the pseudo-tree obtained by using a DFS visit with the MCN heuristic. Start from node x 1 ; give the dimension of the biggest message exchanged by the algorithm (in terms of values stored in the table); compute the total number of messages that DPOP would use to solve this problem. In general, is this number dependent on the pseudo-tree used ?

DPOP: 30 Apr. 2014 (partial test) Exercises, II Consider the following binary cost network: Variables, part = { x 1 , x 2 , x 3 , x 4 , x 5 } , Domains, D 1 = { G , B } , D 2 = D 3 = X = = { R , B } , Constraints = { } and = D 4 D 5 C h C s { F 12 ( x 1 , x 2 ) , F 13 ( x 1 , x 3 ) , F 14 ( x 1 , x 4 ) , F 15 ( x 1 , x 5 ) , F 23 ( x 2 , x 2 ) , F 35 ( x 3 , x 5 ) } . Where each F ij has the following form � − 1 if values are the same F ij ( x i , x j ) = 0 otherwise Consider the PseudoTrees that correspond to the following DFS visit orders o 1 = { x 5 , x 1 , x 4 , x 2 , x 3 } and o 2 = { x 1 , x 4 , x 3 , x 2 , x 5 } . Answer the following questions: state which order is better considering message size and computation, motivate your answer. solve the problem by using the DPOP algorithm with a PseudoTree of your choice.