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CS 540: Introduction to Artificial Intelligence

Final Exam: 12:25-2:25pm, December 16, 2002

Room 168 Noland

CLOSED 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 of

these sheets for scratch work.

Write your name on this and all other pages of this exam. Make sure your exam contains six problems on

ten 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 sentence

is ambiguous, clarify which meaning you’re representing in logic. (Write your answers

below 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 is

now owned by Mary). [You must use situation calculus here.]

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Name: _____________________________

b) Provide a formal interpretation that shows that the following translation from English to

FOPC is incorrect. Be sure to explain your answer formally using the interpretation you

provide.

A book of Sue’s is missing. !x [ book(x) " owner(x, Sue) ] # missing(x)

c) What is the most-general unifier (mgu) of these two wff’s? ____________________

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 function

as its activation function. All the initial weights and the bias (“threshold”) equal 0.1. Assume

the 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 this

training example. Let $ (the learning rate) be 0.2 and be sure to adjust the output unit’s bias

during training.

Perceptron BEFORE Training

Perceptron AFTER Training

b) Qualitatively draw a (2D) picture of weight space where the backprop algorithm is likely to

i. do well

ii. do poorly

Be sure to explain your answers.

4

Name: _____________________________

Problem 3 –Miscellaneous Questions (20 points)

a) What do you feel are the two (2) most important design choices you would need to make if

you used CBR to choose the location of your next vacation? Briefly justify your answers.

i. ______________________________________________________________

ii. ______________________________________________________________

b) In a weird dream, you’re the simulated annealing algorithm. Currently you’re at node A in a

search space; g(A) = 7 and h(A) = 5. You next randomly select node B; g(B) = 9 and

h(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.

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Name: _____________________________

d) On your way out of the hit feature To Build a Decision Tree, you are surprised to find out the

movie theater is giving away prizes. You watch the people ahead of you choose their prize

either 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 chose

Door #2 got $10.

Assuming you want to maximize the likely dollar value of your prize, what door should you

choose? ______________ Why?

e) Consider the joint probability distribution below.

A B C P(A, B, C)

False False False 0.05

False False True 0.10

False True False 0.03

False True True 0.25

True False False 0.15

True False True 0.02

True True False 0.07

True True True 0.33

i. What is P(A = true)? ______________ Show your work below.

ii. What is P(A # B)? ______________ Explain.

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Name: _____________________________

Problem 4 – Important AI Concepts (10 points)

Describe each of the following AI concepts and briefly explain its most significant aspect. (Write

your answers in the space below the AI concept.)

Soundness

Overfitting

Fitness Functions

Vector-Space Model

Negation by Failure

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Name: _____________________________

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 0.1

false true 0.5

true false 0.4

true true 0.9

B C P(D=true | B, C)

false false 0.8

false true 0.6

true false 0.3

true true 0.1

A P(A=true) = 0.2 B P(B=true) = 0.7

C

D

a) 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? _______________

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Name: _____________________________

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, at

any point in time 2% of all people have red eyes, and at any point in time 1% of the

population 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 M’s variables have three possible

values (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 times

M2=low 10 times, M2=med 80 times, and M2 = high 10 times

D was false 200 times and for these cases:

M1=low 20 times, M1=med 80 times, and M1 = high 100 times

M2=low 180 times, M2=med 10 times, and M2 = high 10 times

Making 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 above

and under the stated assumptions. [Do this algebraically – i.e., as an equation.]

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Name: _____________________________

ii. On a new episode we find M1=low and M2=low. What is the most likely

diagnosis? ______________ This time justify your answer numerically.

iii. Draw the Bayesian network that one would construct from the above data (do not

add any “pseudo” counts to the above statistics; we won’t worry about dealing with

probabilities equaling zero). Be sure to explain your solution.

Have a good vacation!

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