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Lower Bounds for Passive and Active Learning
Maxim Raginsky · Sasha Rakhlin

Wed Dec 14 03:48 AM -- 03:52 AM (PST) @ None

We develop unified information-theoretic machinery for deriving lower bounds for passive and active learning schemes. Our bounds involve the so-called Alexander's capacity function. The supremum of this function has been recently rediscovered by Hanneke in the context of active learning under the name of ""disagreement coefficient."" For passive learning, our lower bounds match the upper bounds of Gine and Koltchinskii up to constants and generalize analogous results of Massart and Nedelec. For active learning, we provide first known lower bounds based on the capacity function rather than the disagreement coefficient.

Author Information

Maxim Raginsky (University of Illinois at Urbana-Champaign)
Sasha Rakhlin (University of Pennsylvania)

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