Reparametrization-covariant theory for on-line learning of probability distributions.
We discuss the on-line learning of probability distributions in a reparametrization covariant formulation. Reparametrization covariance plays an essential role not only to respect an intrinsic property of "information" but also for pattern recognition problems. We can obtain an optimal on-line learning algorithm with reparametrization invariance, where the conformal gauge connects a covariant formulation with a noncovariant one in a natural way.
Aida
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Tokyo Metropolitan College of Aeronautical Engineering, Minami-senjyu, Arakawa-ku, Tokyo 116-0003, Japan.