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A system that learns to predict events in various environments is described. The system is associative and distributed; a hierarchical self-organization of low-level units into high-level units takes place based on experience in a particular domain. Its design is inspired by widely held principles of brain organization and by some newly developed techniques in nonparametric statistical inference. The system can be regarded as a realization of a nonparametric statistical algorithm. This is demonstrated by a discussion of system architecture and a presentation of an application in a `number theory' environment.