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How
many distinct decision trees with n Boolean
attributes?
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= number of
Boolean functions
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= number of
distinct truth tables with 2n rows = 22n
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E.g., with 6
Boolean attributes, there are
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18,446,744,073,709,551,616
trees
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How
many purely conjunctive hypotheses (e.g., Hungry Rain)?
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Each attribute
can be in (positive), in (negative), or out
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3n distinct conjunctive hypotheses
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| n |
More expressive
hypothesis space
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¡ |
increases chance
that target function can be expressed
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¡ |
increases number
of hypotheses consistent with training set
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may get worse predictions
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