Case-based learning in inductive inference

ABSTRACT

There is proposed a formalization of case-based learning in terms of recursion-theoretic inductive inference. This approach is directly derived from some recently published case-based learning algorithms. The intention of the present paper is to exhibit the relationship between case-based learning and inductive inference and to specify this relation with mathematical precision. In particular, it is the author's intention to invoke inductive inference results for pointing to the crucial questions in case-based learning which allow to improve the power of case-based learning algorithms considerably. There are formalized several approaches to case-based learning. First, they vary in the way of presenting cases to a learning algorithm. Second, they are different with respect to the underlying semantics of case bases together with similarity measures. Third, they are distinguished by the flexibility in using similarity functions. The investigations presented relate the introduced learning types to identification types in recursion-theoretic inductive inference.

REFERENCES

• Aha91: David W. Aha Case-Based Learning Algorithms in: Proc. DARPA Workshop on Case-based Reasoning, Morgan Kaufmann Publ., 1991, 147-157
• AKA91: David W. Aha , Dennis Kibler , Marc K. Albert, Instance-Based Learning Algorithms, Machine Learning, v.6 n.1, p.37-66, Jan. 1991 [doi>10.1023/A:1022689900470]
• AS83: Dana Angluin , Carl H. Smith, Inductive Inference: Theory and Methods, ACM Computing Surveys (CSUR), v.15 n.3, p.237-269, Sept. 1983 [doi>10.1145/356914.356918]
• Jan91: Klaus P. Jantke, Monotonic and non-monotonic inductive inference, New Generation Computing, v.8 n.4, p.349-360, 1991 [doi>10.1007/BF03037092]
• JB81: Klaus P. Jantke and Hans-Rainer Beick Combining Postulates of Naturalness in Inductive Inference EIK 17 (1981) 8/9, 465484

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.6 Learning
          Subjects: Induction

General Terms:
Algorithms, Theory, Verification