Sample problems from second half of course

Let me emphasize that this is just a collection of sample problems, not a sample final exam.

Multiple choice problems

Problem 1

Bayes' Law states that

Problem 2

In Naive Bayes learning, we make the assumption that

Problem 3

A support vector machine finds a linear separator that maximizes the "margin", which is:

Problem 4

In the problem of tag elements E1 ... EN with tags T1 ... TN, the K-gram assumption is the assumption that




Problem 5

Learning takes place in a back-propagation network by

Long Answer Problems

Problem 6

A. What conditional probabilities are recorded in the above Bayesian network?

B. For each of the following statements, say whether it is true or false in the above network:

  • B and C are independent absolutely.
  • B and C are independent given A.
  • B and C are independent given D.
  • A and D are independent absolutely.
  • A and D are independent given B.
  • A and D are independent given B and C.

    C. Assuming that all the random variables are Boolean, show how Prob(B=T) can be calculated in terms of the probabilities recorded in the above network.

    Problem 7

    Datasets often contain instances with null values in some of the attributes. Some classification learning algorithms are able to use such instances in the training set; other algorithms must discard them.
    
    
    
    
    
    
    

    Problem 8

    The version of the ID3 algorithm in the class handout includes a test "If AVG_ENTROPY(AS,C,T) is not substantially smaller than ENTROPY(C,T)'' then the algorithm constructs a leaf corresponding to the current state of T and does not recur. "Substantially smaller" here, of course, is rather vague. Is overfitting more likely to occur if this condition is changed to require that "AVG_ENTROPY(AS,C,T) is much smaller than ENTROPY(C,T)" or if the condition is changed to "AVG_ENTROPY(AS,C,T) is at all smaller than ENTROPY(C,T)"? Explain your answer. the disadvantage of eliminating the test?

    Problem 9

    Problem 10

    The most common measure of the quality of a classifier is in terms of the accuracy of its predictions. Explain why this is not always the best measure and describe an alternative measure.