On the inductive inference of recursive real-valued functions

Apsĩis, Kalvis; Arikawa, Setsuo; Freivalds, Rūsiņš; Hirowatari, Eiju; Smith, Carl H.

doi:10.1016/s0304-3975(98)00281-3

Cited by 5 publications

(2 citation statements)

References 8 publications

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“…However, the exact location of the class of limiting partial recursively enumerable sets in the arithmetical hierarchy was not deÿned by Gold. Later the idea of functions computed in the limit was transformed into the construction of algorithmic inductive inference and learning in the limit [17]. The development of this direction brought researchers to the following concept (e.g., [5]). …”

Section: Deÿnitionmentioning

confidence: 99%

Experience, generations, and limits in machine learning

Burgin

Klinger

2004

Theoretical Computer Science

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This paper extends traditional models of machine learning beyond their one-level structure by introducing previously obtained problem knowledge into the algorithm or automaton involved. Some authors studied more advanced than traditional models that utilize some kind of predetermined knowledge, having a two-level structure. However, even in this case, the model has not re ected the source and inherited properties of predetermined knowledge. In society, knowledge is often transmitted from previous generations. The aim of this paper is to construct and study algorithmic models of learning processes that utilize predetermined or prior knowledge. The models use recursive, subrecursive, and super-recursive algorithms. Predetermined knowledge includes: a text description, activity rules (e.g., for cognition), and speciÿc structured personal or social memory. Algorithmic models represent these three forms as separate structured processing systems: automata with (1) advice; (2) structured program; and (3) structured memory. That yields three basic models for learning systems: polynomially bounded turing machines, Turing machines, and inductive Turing machines of the ÿrst order.

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Section: Deÿnitionmentioning

confidence: 99%

Experience, generations, and limits in machine learning

Burgin

Klinger

2004

Theoretical Computer Science

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“…However, analysis of learning for continuous objects, such as classification, regression, and clustering for multivariate data, with Gold's model is still under development, despite such settings being typical in modern machine learning. To the best of our knowledge, the only line of studies devoted to learning of real-valued functions was by Arikawa (1997, 2001) Apsītis et al (1999), Hirowatari et al (2003Hirowatari et al ( , 2005Hirowatari et al ( , 2006, where they addressed the analysis of learnable classes of real-valued functions using computable representations of real numbers. 2 We therefore need a new theoretical and computational framework for modern machine learning based on Gold's learning model with discretization of numerical data.…”

Section: Introductionmentioning

confidence: 99%