Name: Rada Vaksman
12/11/2010
2.4. Consider the instance space consisting of integer points in the x, y plane and the set of
hypotheses H consisting of rectangles. More precisely, hypotheses are of the form
a
≤
x
≤
b, c
≤
y
≤
d, where a, b, c, and d can be any integers.
(a) Consider the version space with respect to the set of positive (+) and negative () training
examples shown below. What is the S boundary of the version space in this case? Write out
the hypotheses and draw them in on the diagram.
S set should contain hypotheses that are most specific that means smallest "integer" rectangle
that contains the positive examples. Consider h=(a,b,c,d) then:
S=(4,6,3,5)
(b) What is the G boundary of this version space? Write out the hypotheses and draw them in.
G set should contain hypotheses that are most general that means largest "integer" rectangle
that contains only
the positive examples. Consider h=(a,b,c,d) then:
G=(3,8,2,7),(2,8,2,5)
(c) Suppose the learner may now suggest a new x, y instance and ask the trainer for its
classification. Suggest a query guaranteed to reduce the size of the version space, regardless
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 Spring '09
 STEPHANIEVIE
 version space, training examples, Rada Vaksman

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