An Unbiased Learner

1. The solution to the problem of assuring that the target concept is in the hypothesis space H is to provide a hypothesis space capable of representing every teachable concept that is representing every possible subset of the instances X.
2. The set of all subsets of a set X is called the power set of X

• In the EnjoySport learning task the size of the instance space X of days described by the six attributes is 96 instances.
• Thus, there are 2⁹⁶ distinct target concepts that could be defined over this instance space and learner might be called upon to learn.
• The conjunctive hypothesis space is able to represent only 973 of these - a biased hypothesis space indeed
•  Let us reformulate the EnjoySport learning task in an unbiased way by defining a new hypothesis space H' that can represent every subset of instances
• The target concept "Sky = Sunny or Sky = Cloudy" could then be described as

 (Sunny, ?, ?, ?, ?, ?) v (Cloudy, ?, ?, ?, ?, ?)