Learning and classifying

We define and study a learning paradigm that sits between identification in the limit and classification. More precisely, we expect that a learner be able to identify in the limit which members of a set D of n possible data belong to a target language, where n and D are arbitrary. We show that Ex- and BC-learning are often more difficult than performing this classification task, taking into account desirable constraints on how the learner behaves, such as bounding the number of mind changes and being conservative. Special attention is given to various forms of consistency. We provide a fairly comprehensive set of results that demonstrate the fruitfulness of the approach and the richness of the paradigm.

[1]  Manuel Blum,et al.  Toward a Mathematical Theory of Inductive Inference , 1975, Inf. Control..

[2]  Thomas Zeugmann,et al.  Learning recursive functions: A survey , 2008, Theor. Comput. Sci..

[3]  Efim Kinber,et al.  On the Classification of Computable Languages , 1997, STACS.

[4]  Sanjay Jain,et al.  Absolute versus probabilistic classification in a logical setting , 2005, Theoretical Computer Science.

[5]  Rusins Freivalds,et al.  An inductive inference approach to classification , 1994, J. Exp. Theor. Artif. Intell..

[6]  Robert H. Sloan,et al.  BOOK REVIEW: "SYSTEMS THAT LEARN: AN INTRODUCTION TO LEARNING THEORY, SECOND EDITION", SANJAY JAIN, DANIEL OSHERSON, JAMES S. ROYER and ARUN SHARMA , 2001 .

[7]  D. C. Cooper,et al.  Theory of Recursive Functions and Effective Computability , 1969, The Mathematical Gazette.

[8]  W. Gasarch,et al.  Bounded Queries in Recursion Theory , 1998 .

[9]  Jr. Hartley Rogers.  Theory of Recursive Functions and Effective Computability , 1969 .

[10]  John Case,et al.  Periodicity in generations of automata , 1974, Mathematical systems theory.

[11]  John Case,et al.  Comparison of Identification Criteria for Machine Inductive Inference , 1983, Theor. Comput. Sci..

[12]  Klaus P. Jantke,et al.  Combining Postulates of Naturalness in Inductive Inference , 1981, J. Inf. Process. Cybern..

[13]  John Case,et al.  Machine Inductive Inference and Language Identification , 1982, ICALP.

[14]  E. Mark Gold,et al.  Language Identification in the Limit , 1967, Inf. Control..

[15]  Carl H. Smith,et al.  Classifying Predicates and Languages , 1997, Int. J. Found. Comput. Sci..

[16]  Carl H. Smith,et al.  Generalization versus classification , 1992, COLT '92.

[17]  Rolf Wiehagen,et al.  Charakteristische Eigenschaften von erkennbaren Klassen rekursiver Funktionen , 1976, J. Inf. Process. Cybern..

[18]  Frank Stephan,et al.  On one-sided versus two-sided classification , 2001, Arch. Math. Log..

[19]  John Case,et al.  On the classification of recursive languages , 2004, Inf. Comput..

[20]  Dana Angluin,et al.  Inductive Inference of Formal Languages from Positive Data , 1980, Inf. Control..

[21]  Daniel N. Osherson,et al.  Criteria of Language Learning , 1982, Inf. Control..

[22]  Sanjay Jain.  On an open problem in classification of languages , 2001, J. Exp. Theor. Artif. Intell..

[23]  Daniel N. Osherson,et al.  Systems That Learn: An Introduction to Learning Theory for Cognitive and Computer Scientists , 1990 .