Learning Families of Closed Sets in Matroids

In this paper it is studied for which oracles A and which types of A-r.e. matroids the class of all A-r.e. closed sets in the matroid is learnable by an unrelativised learner. The learning criteria considered comprise in particular criteria more general than behaviourally correct learning, namely behaviourally correct learning from recursive texts, partial learning and reliably partial learning. For various natural classes of matroids and learning criteria, characterisations of learnability are obtained.

[1]  E. Maier.  New Frontiers in Artificial Intelligence , 2009 .

[2]  Eliana Minicozzi,et al.  Some Natural Properties of Strong-Identification in Inductive Inference , 1976, Theor. Comput. Sci..

[3]  A. Nerode,et al.  Recursively enumerable vector spaces , 1977 .

[4]  Iraj Kalantari,et al.  Maximal Vector Spaces Under Automorphisms of the Lattice of Recursively Enumerable Vector Spaces , 1977, J. Symb. Log..

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

[6]  Akihiro Yamamoto,et al.  Topological properties of concept spaces (full version) , 2010, Inf. Comput..

[7]  Wojciech Rytter,et al.  On the Maximal Number of Cubic Runs in a String , 2010, LATA.

[8]  Cristian S. Calude.  Information and Randomness: An Algorithmic Perspective , 1994 .

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

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

[11]  Frank Stephan,et al.  Learning algebraic structures from text , 2001, Theor. Comput. Sci..

[12]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[13]  R. Soare,et al.  Π⁰₁ classes and degrees of theories , 1972 .

[14]  Akihiro Yamamoto,et al.  Inferability of Closed Set Systems from Positive Data , 2006, JSAI.

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

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

[17]  Akihiro Yamamoto,et al.  Topological Properties of Concept Spaces , 2008, ALT.

[18]  Marcia J. Groszek,et al.  Pi0a Classes and Minimal Degrees , 1997, Ann. Pure Appl. Log..

[19]  Frank Stephan,et al.  On the learnability of vector spaces , 2007, J. Comput. Syst. Sci..

[20]  A. Nerode,et al.  Recursion Theory on Fields and Abstract Dependence , 1980 .

[21]  John Case,et al.  Synthesizing Learners Tolerating Computable Noisy Data , 2001, J. Comput. Syst. Sci..

[22]  R. Soare.  Recursively enumerable sets and degrees , 1987 .

[23]  P. Odifreddi.  Classical recursion theory , 1989 .

[24]  Cristian S. Calude.  Relativized Topological Size of Sets of Partial Recursive Functions , 1991, Theor. Comput. Sci..

[25]  Timo Kötzing,et al.  String Extension Learning Using Lattices , 2010, LATA.

[26]  C. Jockusch.  Degrees in Which the Recursive Sets are Uniformly Recursive , 1972, Canadian Journal of Mathematics.

[27]  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 .

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

[29]  Alexander Raichev.  A MINIMAL RK-DEGREE , 2008 .

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

[31]  Mark A. Fulk.  Prudence and Other Conditions on Formal Language Learning , 1990, Inf. Comput..