Consider a concept learning problem in which each instance is a real number, and in which each hypothesis is an interval over the reals. More precisely, each hypothesis in the hypothesis space H is of the form a

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Consider a concept learning problem in which each instance is a real number, and in
which each hypothesis is an interval over the reals. More precisely, each hypothesis
in the hypothesis space H is of the form a <x<b, where a and b are any real
constants, and x refers to the instance. For example, the hypothesis 4.5 < x < 6.1
classifies instances between 4.5 and 6.1 as positive, and others as negative. Explain
informally why there cannot be a maximally specific consistent hypothesis for any
set of positive training examples. Suggest a slight modification to the hypothesis
representation so that there will be.
Transcribed Image Text:Consider a concept learning problem in which each instance is a real number, and in which each hypothesis is an interval over the reals. More precisely, each hypothesis in the hypothesis space H is of the form a <x<b, where a and b are any real constants, and x refers to the instance. For example, the hypothesis 4.5 < x < 6.1 classifies instances between 4.5 and 6.1 as positive, and others as negative. Explain informally why there cannot be a maximally specific consistent hypothesis for any set of positive training examples. Suggest a slight modification to the hypothesis representation so that there will be.
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