Sample Exam Problems

The final exam will be given Thursday, May 7 from 5:00 to 6:50 in Warren Weaver, room 101. It is closed book and closed notes. You will not need a calculator.

Topics covered

You should know the following algorithms well enough to carry them out: depth-first search; breadth-first search; iterative deepening; hill-climbing; game tree evaluation with alpha-beta pruning; Davis-Putnam algorithm; conversion to clausal form and resolution theorem proving for both propositional calculus and predicate calculus; forward-chaining over Horn clauses; backward chaining over Horn clauses; Naive Bayes learning; 1R learning; nearest-neighbors learning.

You should understand the following algorithms well, though I would not ask you to carry them out on an exam: GSAT; simulating annealing; ID3 (called "DECISION-TREE-LEARNING in R+N, p. 658); perceptron learning; feed-forward back-propagation neural networks.

Problem 1:

Name three conditions that must hold on a game for the technique of MIN-MAX game-tree evaluation to be applicable.

Problem 2:

What is the result of doing alpha-beta pruning in the game tree shown below?

Problem 3:

Consider a domain where the individuals are people and languages. Let L be the first-order language with the following primitives:
s(X,L) --- Person X speaks language L. 
c(X,Y) --- Persons X and Y can communicate. 
i(W,X,Y) --- Person W can serve as an interpreter between persons X and Y. 
j,p,e,f --- Constants: Joe, Pierre, English, and French respectively.
A. Express the following statements in L: B. Show how (vi) can be proven from (i)---(v) using backward-chaining resolution. You must show the Skolemized form of each statement, and every resolution that is used in the final proof. You need not show the intermediate stages of Skolemization, or show resolutions that are not used in the final proof.

Problem 4:

Let A, B, C be Boolean random variables. Assume that
Prob(A=T) = 0.8
Prob(B=T | A=T) = 0.5.
Prob(B=T | A=F) = 1.
Prob(C=T | B=T) = 0.1
Prob(C=T | B=F) = 0.5
A and C are conditionally independent given B.
Evaluate the following terms. (If you wish, you can give your answer as an arithmetic expression such as "0.8*0.5 / (0.8*1 + 0.5*0.1)")

Problem 5:

A. Give an example of a decision tree with two internal nodes (including the root), and explain how it classifies an example.
B. Describe the ID3 algorithm to construct decision trees from training data.
C. What is the entropy of a classification C in table T? What is the expected entropy of classification C if table T is split on predictive attribute A?
D. What kinds of techniques can be used to counter the problem of over-fitting in decision trees?

Problem 6:

Consider the following data set with three Boolean predictive attributes, W,X,Y and Boolean classification C.
  W   X   Y   C
----------------
  T   T   T   T
  T   F   T   F
  T   F   F   F
  F   T   T   F
  F   F   F   T
We now encounter a new example: W=F, X=T, Y=F. If we apply the Naive Bayes method, what probability is assigned to the two values of C?

Problem 7:

"Local minima can cause difficulties for a feed-forward, back-propagation neural network." Explain. Local minima of what function of what arguments? Why do they create difficulties?

Problem 8:

Which of the following describes the process of task execution (classifying input signal) in a feed-forward, back-propagation neural network? Which describe the process of learning? (One answer is correct for each.)

Problem 9

Explain briefly (2 or 3 sentences) the use of a training set and a test set in evaluating learning programs.

Problem 10

Explain how the minimum description length (MDL) learning theory justifies the conjecture of
A. perfect classification hypotheses (i.e. classification hypotheses that always give the correct classification, given the values of the predictive attributes) for nominal classifications.
B. imperfect classification hypotheses (i.e. hypotheses that do better than chance) for nominal attributes.
C. approximate classification hypotheses for numeric classifications. (i.e. hypotheses that give answers that are nearly correct.)