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Trading monotonicity demands versus mind changes

  • Steffen Lange
  • Thomas Zeugmann
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 904)

Abstract

The present paper deals with with the learnability of indexed families \({\cal L}\) of uniformly recursive languages from positive data. We consider the influence of three monotonicity demands to the efficiency of the learning process. The efficiency of learning is measured in dependence on the number of mind changes a learning algorithm is allowed to perform. The three notions of monotonicity reflect different formalizations of the requirement that the learner has to produce better and better generalizations when fed more and more data on the target concept.

We distinguish between exact learnability (\({\cal L}\) has to be inferred with respect to \({\cal L}\)), class preserving learning (\({\cal L}\) has to be inferred with respect to some suitable chosen enumeration of all the languages from \({\cal L}\)), and class comprising inference (\({\cal L}\) has to be learned with respect to some suitable chosen enumeration of uniformly recursive languages containing at least all the languages from \({\cal L}\)).

In particular, we prove that a relaxation of the relevant monotonicity requirement may result in an arbitrarily large speed-up.

Keywords

Initial Segment Inductive Inference Hypothesis Space Monotonicity Constraint Computational Learn Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Steffen Lange
    • 1
  • Thomas Zeugmann
    • 2
  1. 1.FB Mathematik und InformatikHTWK LeipzigLeipzig
  2. 2.Research Institute of Fundamental Information ScienceKyushu University 33FukuokaJapan

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