Reference Work Entry

Encyclopedia of Machine Learning

pp 210-219

Connections Between Inductive Inference and Machine Learning

  • John Case
  • , Sanjay Jain


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

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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