Measuring teachability using variants of the teaching dimension

In a typical algorithmic learning model, a learner has to identify a target object from partial information. Conversely, in a teaching model a teacher has to give information that allows the learners to identify a target object. We devise two variants of the classical teaching model for Boolean concept classes, based on the teaching dimension, and describe them by teaching-dimension-like combinatorial parameters. In the first model, the learners choose consistent hypotheses with least complexity. We show that 1-decision lists are the harder to teach the longer they are and that 2-term DNFs are the harder to teach the more terms they have. This contrasts with the teachability results for these classes in the teaching-dimension model. In our second model, the learners choose consistent hypotheses based on the assumption that the teacher is optimal. We show that monomials can be taught with a linear number of examples, whereas some 1-decision lists need exponentially many.

[1]  Dana Angluin,et al.  Teachers, learners and black boxes , 1997, COLT '97.

[2]  Sanjay Jain,et al.  Learning of R.E. Languages from Good Examples , 1997, ALT.

[3]  Toshihide Ibaraki,et al.  Decision lists and related Boolean functions , 2002, Theor. Comput. Sci..

[4]  B. Natarajan.  Machine Learning: A Theoretical Approach , 1992 .

[5]  Rocco A. Servedio,et al.  On the limits of efficient teachability , 2001, Inf. Process. Lett..

[6]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[7]  Ronald L. Rivest,et al.  Being taught can be faster than asking questions , 1995, COLT '95.

[8]  John Shawe-Taylor,et al.  On Specifying Boolean Functions by Labelled Examples , 1995, Discret. Appl. Math..

[9]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

[10]  Ruth C. Carter,et al.  Teachers , 2002, Global Education Monitoring Report 2020.

[11]  Tibor Hegedűs,et al.  Generalized teaching dimensions and the query complexity of learning , 1995, Annual Conference Computational Learning Theory.

[12]  Rusins Freivalds,et al.  On the Power of Inductive Inference from Good Examples , 1993, Theor. Comput. Sci..

[13]  Ayumi Shinohara,et al.  Teachability in computational learning , 1990, New Generation Computing.

[14]  Sally A. Goldman,et al.  Teaching a Smarter Learner , 1996, J. Comput. Syst. Sci..

[15]  D. Angluin.  Queries and Concept Learning , 1988 .

[16]  Ronald L. Rivest,et al.  Learning Binary Relations and Total Orders , 1989, COLT 1989.

[17]  Leslie G. Valiant,et al.  A theory of the learnable , 1984, CACM.

[18]  Rocco A. Servedio,et al.  DNF Are Teachable in the Average Case , 2006, COLT.

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

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

[21]  Tao Jiang,et al.  Lower Bounds on Learning Decision Lists and Trees , 1995, Inf. Comput..

[22]  Hans Ulrich Simon,et al.  Learning decision lists and trees with equivalence-queries , 1995, EuroCOLT.

[23]  Leslie G. Valiant,et al.  Computational limitations on learning from examples , 1988, JACM.

[24]  R. Rivest.  Learning Decision Lists , 1987, Machine Learning.

[25]  Eyal Kushilevitz,et al.  Witness Sets for Families of Binary Vectors , 1996, J. Comb. Theory, Ser. A.

[26]  Andrew Tomkins,et al.  A computational model of teaching , 1992, COLT '92.

[27]  Dana Angluin,et al.  Learning from Different Teachers , 2004, Machine Learning.

[28]  Tibor Hegedüs.  Combinatorial Results on the Complexity of Teaching and Learning , 1994, MFCS.

[29]  Frank J. Balbach,et al.  Teaching Classes with High Teaching Dimension Using Few Examples , 2005, COLT.

[30]  M. Kearns,et al.  On the complexity of teaching , 1991, COLT '91.

[31]  Shai Ben-David,et al.  Self-Directed Learning and Its Relation to the VC-Dimension and to Teacher-Directed Learning , 2004, Machine Learning.

[32]  H. David Mathias,et al.  A Model of Interactive Teaching , 1997, J. Comput. Syst. Sci..

[33]  Christian Kuhlmann.  On Teaching and Learning Intersection-Closed Concept Classes , 1999, EuroCOLT.

[34]  Bernd Becker,et al.  How robust is the n-cube? , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[35]  John Shawe-Taylor,et al.  On exact specification by examples , 1992, COLT '92.