### Probabilistic inductive inferenceProbabilistic inductive inference

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 Author Pitt, L. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1989 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract Inductive inference machines construct programs for total recursive functions given only example values of the functions. $\textit{Probabilistic}$ inductive inference machines are defined, and for various criteria of successful inference, it is asked whether a probabilistic inductive inference machine can infer larger classes of functions if the inference criterion is relaxed to allow inference with probability at least $\textit{p},$ (0 < $\textit{p}$ < 1) as opposed to requiring certainty. For the most basic criteria of success $(\textit{EX}$ and $\textit{BC}),$ it is shown that any class of functions that can be inferred from examples with probability exceeding 1/2 can be inferred deterministically, and that for probabilities $\textit{p}$ ≤ 1/2 there is a discrete hierarchy of inferability parameterized by $\textit{p}.$ The power of probabilistic inference strategies is characterized by equating the classes of probabilistically inferable functions with those classes that can be inferred by $\textit{teams}$ of inductive inference machines (a parallel model of inference), or by a third model called $\textit{frequency}$ inference. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1989-04-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 36 Issue Number 2 Page Count 51 Starting Page 383 Ending Page 433

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Source: ACM Digital Library