” CS 540编程语言 写作、 辅导JavaCS 540: Introduction to Artificial IntelligenceFinal Exam: 12:25-2:25pm, December 16, 2002Room 168 NolandCLOSED BOOK(two sheets of notes and a calculator allowed)Write your answers on these pages and show your work. If you feel that a question is not fully specified,state any assumptions that you need to make in order to solve the problem. You may use the backs ofthese sheets for scratch work.Write your name on this and all other pages of this exam. Make sure your exam contains six problems onten pages.Problem 1 Representing and Reasoning with Logic (28 points)a) Convert each of the following English sentences into First-Order Predicate Calculus(FOPC), using reasonably Named predicates, functions, and constants. If you feel a sentenceis ambiguous, clarify which meaning youre representing in logic. (Write your answersbelow each English sentence.)All birds can fly except for penguins and ostriches or unless they have a broken wing.There was a student in CS 540 Fall 1999 who was born in a country in South America.John sold Mary his CS 540 textbook (and, hence, this book that John formerly owned isnow owned by Mary). [You must use situation calculus here.]2Name: _____________________________b) Provide a formal interpretation that shows that the following translation from English toFOPC is incorrect. Be sure to explain your answer formally using the interpretation youprovide.A book of Sues is missing. !x [ book(x) owner(x, Sue) ] # missing(x)c) What is the most-general unifier (mgu) of these two wffs? ____________________Show your work.d) Why is And Elimination a legal inference rule but Or Elimination is not?Problem 2 Neural Networks (12 points)a) Consider a perceptron that has two real-valued inputs and an output unit with a step functionas its activation function. All the initial weights and the bias (threshold) equal 0.1. Assumethe teacher has said that the output should be 0 for the input in1 = 5 and in2 = -3.Show how the Perceptron learning rule would alter this neural network upon processing thistraining example. Let $ (the learning rate) be 0.2 and be sure to adjust the output units biasduring training.Perceptron BEFORE TrainingPerceptron AFTER Trainingb) Qualitatively draw a (2D) picture of weight space where the backprop algorithm is likely toi. do wellii. do poorlyBe sure to explain your answers.4Name: _____________________________Problem 3 Miscellaneous Questions (20 points)a) What do you feel are the two (2) most important design choices you would need to make ifyou used CBR to choose the location of your next vacation? Briefly justify your answers.i. ______________________________________________________________ii. ______________________________________________________________b) In a weird dream, youre the simulated annealing algorithm. Currently youre at node A in asearch space; g(A) = 7 and h(A) = 5. You next randomly select node B; g(B) = 9 andh(B) = 8. The temperature is a Wisconsin-like 10 degrees.Do you move to node B? _________ Show your work. (Lower h values are better.)c) Show an example of a cross over for a GA whose individuals/entities are 6-bits long.5Name: _____________________________d) On your way out of the hit feature To Build a Decision Tree, you are surprised to find out themovie theater is giving away prizes. You watch the people ahead of you choose their prizeeither from behind Door #1 or Door #2. Of those who chose Door #1, half received $5, 1%got a new bike Worth $1000, and the rest got a worthless movie poster. Everyone who choseDoor #2 got $10.Assuming you want to maximize the likely dollar value of your prize, what door should youchoose? ______________ Why?e) Consider the joint probability distribution below.A B C P(A, B, C)False False False 0.05False False True 0.10False True False 0.03False True True 0.25True False False 0.15True False True 0.02True True False 0.07True True True 0.33i. What is P(A = true)? ______________ Show your work below.ii. What is P(A # B)? ______________ Explain.6Name: _____________________________Problem 4 Important AI Concepts (10 points)Describe each of the following AI concepts and briefly explain its most significant aspect. (Writeyour answers in the space below the AI concept.)SoundnessOverfittingFitness FunctionsVector-Space ModelNegation by Failure7Name: _____________________________Problem 5 Bayesian Networks (12 points)Consider the following Bayesian Network, where variables A-D are all Boolean-valued:A B P(C =true | A, B)false false 0.1false true 0.5true false 0.4true true 0.9B C P(D=true | B, C)False false 0.8false true 0.6true false 0.3true true 0.1A P(A=true) = 0.2 B P(B=true) = 0.7CDa) What is the probability that all four of these Boolean variables are false? ______________b) What is the probability that C is true, D is false, and B is true? _______________c) What is the probability that C is true given that D is false and B is true? _______________8Name: _____________________________Problem 6 More Probabilistic Reasoning (18 points)a) Imagine that 99% of the time RE Disease (RED) causes red eyes in those with the disease, atany point in time 2% of all people have red eyes, and at any point in time 1% of thepopulation has RED.You have red eyes. What is the probability you have RED? _______________b) Assume we have one diagnostic random variable (call it D) and two measurement variables(call them M1 and M2). For simplicity, assume that the Ms variables have three possiblevalues (e.g., low, Medium, and high) and that D is Boolean-valued.We collect data on 300 episodes and find out the following:D was true 100 times and for these cases:M1=low 50 times, M1=med 30 times, and M1 = high 20 timesM2=low 10 times, M2=med 80 times, and M2 = high 10 timesD was false 200 times and for these cases:M1=low 20 times, M1=med 80 times, and M1 = high 100 timesM2=low 180 times, M2=med 10 times, and M2 = high 10 timesMaking the assumption that M1 and M2 are conditionally independent given D,i. Show how Bayes rule Can be used to compute P(D | M1, M2) given the data aboveand under the stated assumptions. [Do this algebraically i.e., as an equation.]9Name: _____________________________ii. On a new episode we find M1=low and M2=low. What is the most likelydiagnosis? ______________ This time justify your answer numerically.iii. Draw the Bayesian network that one would construct from the above data (do notadd any pseudo counts to the above statistics; we wont worry about dealing withprobabilities equaling zero). Be sure to Explain your solution.Have a good vacation!请加QQ：99515681 或邮箱：99515681@qq.com WX：codehelp
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