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machine_learning_exercise2

# machine_learning_exercise2 - Name Rada Vaksman 2.4 Consider...

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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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