Reparametrization-covariant theory for on-line learning of probability distributions - art. no. 056128

We discuss the on-line learning of probability distributions in a reparamet rization covariant formulation. Reparametrization covariance plays an essen tial role not only to respect an intrinsic property of "information" but al so for pattern recognition problems. We can obtain an optimal on-line learn ing algorithm with reparametrization invariance, where the conformal gauge connects a covariant formulation with a noncovariant one in a natural way.