One-Shot Learners Using Negative Counterexamples and Nearest Positive Examples

As some cognitive research suggests, in the process of learning languages, in addition to overtexplicit negative evidence, a child often receives covertexplicit evidence in form of corrected or rephrased sentences. In this paper, we suggest one approach to formalization of overt and covert evidence within the framework of one-shotlearners via subset and membership queries to a teacher (oracle). We compare and explore general capabilities of our models, as well as complexity advantages of learnability models of one type over models of other types, where complexity is measured in terms of number of queries. In particular, we establish that "correcting" positive examples give sometimes more power to a learner than just negative (counter)examples and access to full positive data.

[1]  Dana Angluin,et al.  Queries and concept learning , 1988, Machine Learning.

[2]  Sanjay Jain,et al.  Iterative Learning from Positive Data and Negative Counterexamples , 2006, ALT.

[3]  Frank Stephan,et al.  On the structure of degrees of inferability , 1993, COLT '93.

[4]  Dana Angluin Queries revisited , 2004, Theor. Comput. Sci..

[5]  Douglas L. T. Rohde,et al.  Language acquisition in the absence of explicit negative evidence: how important is starting small? , 1999, Cognition.

[6]  J. Davenport Editor , 1960 .

[7]  Thomas Zeugmann,et al.  A Guided Tour Across the Boundaries of Learning Recursive Languages , 1995, GOSLER Final Report.

[8]  Sanjay Jain,et al.  Learning languages from positive data and negative counterexamples , 2008, J. Comput. Syst. Sci..

[9]  Manuel Blum,et al.  A Machine-Independent Theory of the Complexity of Recursive Functions , 1967, JACM.

[10]  Sanjay Jain,et al.  Gold-Style and Query Learning Under Various Constraints on the Target Class , 2005, ALT.

[11]  Sandra Zilles,et al.  Relations between Gold-style learning and query learning , 2005, Inf. Comput..

[12]  Sanjay Jain,et al.  One-shot learners using negative counterexamples and nearest positive examples , 2009, Theor. Comput. Sci..

[13]  Carl H. Smith,et al.  Learning via queries , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[14]  Leonor Becerra-Bonache,et al.  Learning Balls of Strings with Correction Queries , 2007, ECML.

[15]  William I. Gasarch,et al.  Inferring answers to queries , 1997, COLT '97.

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

[17]  Sandra Zilles,et al.  Formal language identification: query learning vs. Gold-style learning , 2004, Inf. Process. Lett..

[18]  L. Becerra-Bonache,et al.  LEARNING DFA FROM CORRECTIONS , 2006 .

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

[20]  Timo Knuutila,et al.  Polynomial Time Algorithms for Learning k -Reversible Languages and Pattern Languages with Correction Queries , 2007, ALT.

[21]  Thomas Zeugmann,et al.  Learning indexed families of recursive languages from positive data: A survey , 2008, Theor. Comput. Sci..

[22]  Leonor Becerra-Bonache,et al.  Learning DFA from Correction and Equivalence Queries , 2006, ICGI.

[23]  Sanjay Jain,et al.  A general comparison of language learning from examples and from queries , 2007, Theor. Comput. Sci..

[24]  Satoshi Kobayashi,et al.  A Characterization of the Language Classes Learnable with Correction Queries , 2007, TAMC.

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

[26]  Stuart A. Kurtz,et al.  Extremes in the Degrees of Inferability , 1994, Ann. Pure Appl. Log..