  This paper describes a family of probabilistic architectures designed for
online learning under the logarithmic loss. Rather than relying on non-linear
transfer functions, our method gains representational power by the use of data
conditioning. We state under general conditions a learnable capacity theorem
that shows this approach can in principle learn any bounded Borel-measurable
function on a compact subset of euclidean space; the result is stronger than
many universality results for connectionist architectures because we provide
both the model and the learning procedure for which convergence is guaranteed.
