17 Mar 2004
CS 3243 - Learning
29
Hypothesis spaces
How many distinct
decision trees with n Boolean attributes?
= number of Boolean functions
= number of distinct truth tables
with 2n rows = 22n
nE.g., with 6 Boolean attributes, there are 18,446,744,073,709,551,616 trees
How many purely
conjunctive hypotheses (e.g., Hungry Ù ØRain)?
nEach attribute can be in (positive), in (negative), or
out
Þ 3n distinct conjunctive hypotheses
nMore expressive hypothesis space
¡increases chance that target function can be
expressed
¡increases number of hypotheses consistent with training
set
Þ may get worse predictions