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Given a collection of models F, suppose you were able to develop an algorithm A: (ifA (that is, given n labeled training samples, A returns
Given a collection of models F, suppose you were able to develop an algorithm A: (ifA (that is, given n labeled training samples, A returns a model fA EF that has the following property: for all e > 0, with probability 0.55 (over the draw of n = 0(5) samples, err(m)-inferr(f) e, fEF where err(f) := Paw) [f(x) Show that one can construct an algorithm B: (xi, yiwith the property: for all > 0 and all > 0, with probability at least 1- over a draw of n, samples: err(-infer(f) . fE.F Moreover show that n' = pol such a model f. Hence, the model class F is efficiently PAC-learnable. (Hint: Algorithm 3 can make multiple calls to the algorithm A.) y( ) samples are enough for the algorithm B to return Given a collection of models F, suppose you were able to develop an algorithm A: (ifA (that is, given n labeled training samples, A returns a model fA EF that has the following property: for all e > 0, with probability 0.55 (over the draw of n = 0(5) samples, err(m)-inferr(f) e, fEF where err(f) := Paw) [f(x) Show that one can construct an algorithm B: (xi, yiwith the property: for all > 0 and all > 0, with probability at least 1- over a draw of n, samples: err(-infer(f) . fE.F Moreover show that n' = pol such a model f. Hence, the model class F is efficiently PAC-learnable. (Hint: Algorithm 3 can make multiple calls to the algorithm A.) y( ) samples are enough for the algorithm B to return
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