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Connections Between Inductive Inference and Machine Learning

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Encyclopedia of Machine Learning

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Definition

Inductive inference is a theoretical framework to model learning in the limit. Here we will discuss some results in inductive inference, which have relevance to machine learning community.

The mathematical/theoretical area called Inductive Inference, is also known as computability theoretic learning and learning in the limit (Jain, Osherson, Royer, & Sharma, 1999; Odifreddi, 1999) typically but, as will be seen below, not always involves a situation depicted in (1) just below.

$$\begin{array}{rcl} \textrm{ Data }{d}_{0},{d}_{1},{d}_{2},\ldots \mathop \to \limits^{{\mathop{\rm In}\nolimits}} M\mathop \to \limits^{{\mathop{\rm Out}\nolimits}} \textrm{ Programs}{e}_{0},{e}_{1},{e}_{2},\ldots.\end{array}$$
(1)

Let \(\mathbb{N} =\) the set of nonnegative integers. Strings, including program strings, computer reals, and other data structures, inside computers, are finite bit strings and, hence, can be coded into \(\mathbb{N}\). Therefore, mathematically at least, it is without...

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    1. John Case
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    2. Sanjay Jain
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    1. School of Computer Science and Engineering, University of New South Wales, Sydney, Australia, 2052

      Claude Sammut

    2. Faculty of Information Technology, Clayton School of Information Technology, Monash University, P.O. Box 63, Victoria, Australia, 3800

      Geoffrey I. Webb

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    Case, J., Jain, S. (2011). Connections Between Inductive Inference and Machine Learning. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30164-8_160

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