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Singer Island, FL

Oct. 24, 1984 to Oct. 26, 1984

ISBN: 0-8186-0591-X

pp: 485-494

L. Pitt , Yale University

ABSTRACT

Inductive Inference Machines (IlMs) attempt to identify functions given only input-output pairs of the functions. Probabilistic IlMs are defined, as is the probability that a probabilistic IlM identifies a function with respect to two common identification criteria: EX and BC. Let ID denote either of these criteria. Then ID/sub prob/(p) is the family of sets of functions U for which there is a probabilistic IlM identifying every f /spl epsi/ U with probability /spl ges/ p. It is shown that for all positive integers n, ID/sub prob/(1/n) is properly contained in ID/sub prob/(1/(n+1)), and that this discrete hierarchy is the "finest" possible. This hierarchy is related to others in the literature.

CITATION

L. Pitt,
"A Characterization Of Probabilistic Inference",

*FOCS*, 1984, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 1984, pp. 485-494, doi:10.1109/SFCS.1984.715951