Rigorous Bounds to Retarded Learning
Arnaud Buhot, Mirta B. Gordon, Jean-Pierre Nadal
Abstract
We show that the lower bound to the critical fraction of data needed to infer (learn) the orientation of the anisotropy axis of a probability distribution, determined by Herschkowitz and Opper [Phys.Rev.Lett. 86, 2174 (2001)], is not always valid. If there is some structure in the data along the anisotropy axis, their analysis is incorrect, and learning is possible with much less data points.
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