We want to learn an unknown monotone conjunction c with n variables. For that, we draw i.i.d. m assignments that are correctly labelled as 0 (false) or 1 (true). We want to use the VC dimension to calculate the sample size for PAC-learnability. (b) Bonus: Prove that the VC dimension of the hypothesis class formed by monotone conjunctions with n variables is at most n. You need to prove that any set of n + 1 assignments cannot be shattered with monotone conjunctions.

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We want to learn an unknown monotone conjunction c with n variables. For that, we draw i.i.d. m assignments that are
correctly labelled as 0 (false) or 1 (true). We want to use the VC dimension to calculate the sample size for PAC-learnability.
(b) Bonus: Prove that the VC dimension of the hypothesis class formed by monotone conjunctions with n variables is
at most n. You need to prove that any set of n + 1 assignments cannot be shattered with monotone conjunctions.
Transcribed Image Text:We want to learn an unknown monotone conjunction c with n variables. For that, we draw i.i.d. m assignments that are correctly labelled as 0 (false) or 1 (true). We want to use the VC dimension to calculate the sample size for PAC-learnability. (b) Bonus: Prove that the VC dimension of the hypothesis class formed by monotone conjunctions with n variables is at most n. You need to prove that any set of n + 1 assignments cannot be shattered with monotone conjunctions.
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