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linear functions) then the sample complexity is finite, and it depends linearly on the VC dimension on the class of target functions.

Definition

Let be a space which we call the input space, and be a space which we call the output space, and let denote the product . For example, in the setting of binary classification, is typically a finite-dimensional vector space and is the set .

Fix a hypothesis space of functions . A learning algorithm over is a computable map from to

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