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Could you please explain what the hypothesis space for decision tree learning look like?

And what is the cardinality of this space?

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As per Tom Mitchell's,

".....For example, consider the space of hypotheses that could in principle be output by the above checkers learner. This hypothesis space consists of all evaluation functions that can be represented by some choice of values for the weights wo through w6. The learner's task is thus to search through this vast space to locate the hypothesis that is most consistent with the available training examples....."

Hence , Basically all possible combination of distinct trees makes the hypothesis space.

Lets say if you have chosen to represent your function to be a linear line then all possible linear lines which go through the data (given input, output) makes up your hypothesis space.

Each tree= Single hypothesis , that says this tree shall best fit my data and predict the correct results

therefore combination of all such possible tress= hypothesis space.

Here is the snippet of PPT from lecture

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