CN = CPCN

Abstract

We address the issue of the learnability of concept classes under three classification noise models in the probably approximately correct framework. After introducing the Class-Conditional Classification Noise (CCCN) model, we investigate the problem of the learnability of concept classes under this particular setting and we show that concept classes that are learnable under the well-known uniform classification noise (CN) setting are also CCCN-learnable, which gives CN = CCCN. We then use this result to prove the equality between the set of concept classes that are CN-learnable and the set of concept classes that are learnable in the Constant Partition Classification Noise (CPCN) setting, or, in other words, we show that CN = CPCN.