For every polynomial p, a VC-dimension-1 concept class needs Θ(p(n)) samples for efficient learning while O(1) samples suffice information-theoretically, assuming NP is exponentially hard.
Trading group theory for randomness
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Computational-Statistical Tradeoffs from NP-hardness
For every polynomial p, a VC-dimension-1 concept class needs Θ(p(n)) samples for efficient learning while O(1) samples suffice information-theoretically, assuming NP is exponentially hard.