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We combine a new data model, where the random classification is subjected to rather weak restrictions which in turn are based on the Mammen−Tsybakov [E. Mammen and A.B. Tsybakov, 27 (1999) 1808–1829; A.B. Tsybakov, 32 (2004) 135–166.] small margin conditions, and the statistical query (SQ) model due to Kearns [M.J. Kearns, 45 (1998) 983–1006] to what we refer to as PAC + SQ model. We generalize the class conditional constant noise (CCCN) model introduced by Decatur [S.E. Decatur, in Morgan Kaufmann...
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