Preference-based Teaching

Ziyuan Gao, Christoph Ries, Hans Simon, Sandra Zilles
; 29th Annual Conference on Learning Theory, PMLR 49:971-997, 2016.

Abstract

We introduce a new model of teaching named “preference-based teaching” and a corresponding complexity parameter—the preference-based teaching dimension (PBTD)—representing the worst-case number of examples needed to teach any concept in a given concept class. Although the PBTD coincides with the well-known recursive teaching dimension (RTD) on finite classes, it is radically different on infinite ones: the RTD becomes infinite already for trivial infinite classes (such as half-intervals) whereas the PBTD evaluates to reasonably small values for a wide collection of infinite classes including classes consisting of so-called closed sets w.r.t. a given closure operator, including various classes related to linear sets over \mathbbN_0 (whose RTD had been studied quite recently) and including the class of Euclidean half-spaces (and some other geometric classes). On top of presenting these concrete results, we provide the reader with a theoretical framework (of a combinatorial flavor) which helps to derive bounds on the PBTD.

Cite this Paper


BibTeX
@InProceedings{pmlr-v49-gao16, title = {Preference-based Teaching}, author = {Ziyuan Gao and Christoph Ries and Hans Simon and Sandra Zilles}, booktitle = {29th Annual Conference on Learning Theory}, pages = {971--997}, year = {2016}, editor = {Vitaly Feldman and Alexander Rakhlin and Ohad Shamir}, volume = {49}, series = {Proceedings of Machine Learning Research}, address = {Columbia University, New York, New York, USA}, month = {23--26 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v49/gao16.pdf}, url = {http://proceedings.mlr.press/v49/gao16.html}, abstract = {We introduce a new model of teaching named “preference-based teaching” and a corresponding complexity parameter—the preference-based teaching dimension (PBTD)—representing the worst-case number of examples needed to teach any concept in a given concept class. Although the PBTD coincides with the well-known recursive teaching dimension (RTD) on finite classes, it is radically different on infinite ones: the RTD becomes infinite already for trivial infinite classes (such as half-intervals) whereas the PBTD evaluates to reasonably small values for a wide collection of infinite classes including classes consisting of so-called closed sets w.r.t. a given closure operator, including various classes related to linear sets over \mathbbN_0 (whose RTD had been studied quite recently) and including the class of Euclidean half-spaces (and some other geometric classes). On top of presenting these concrete results, we provide the reader with a theoretical framework (of a combinatorial flavor) which helps to derive bounds on the PBTD.} }
Endnote
%0 Conference Paper %T Preference-based Teaching %A Ziyuan Gao %A Christoph Ries %A Hans Simon %A Sandra Zilles %B 29th Annual Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2016 %E Vitaly Feldman %E Alexander Rakhlin %E Ohad Shamir %F pmlr-v49-gao16 %I PMLR %J Proceedings of Machine Learning Research %P 971--997 %U http://proceedings.mlr.press %V 49 %W PMLR %X We introduce a new model of teaching named “preference-based teaching” and a corresponding complexity parameter—the preference-based teaching dimension (PBTD)—representing the worst-case number of examples needed to teach any concept in a given concept class. Although the PBTD coincides with the well-known recursive teaching dimension (RTD) on finite classes, it is radically different on infinite ones: the RTD becomes infinite already for trivial infinite classes (such as half-intervals) whereas the PBTD evaluates to reasonably small values for a wide collection of infinite classes including classes consisting of so-called closed sets w.r.t. a given closure operator, including various classes related to linear sets over \mathbbN_0 (whose RTD had been studied quite recently) and including the class of Euclidean half-spaces (and some other geometric classes). On top of presenting these concrete results, we provide the reader with a theoretical framework (of a combinatorial flavor) which helps to derive bounds on the PBTD.
RIS
TY - CPAPER TI - Preference-based Teaching AU - Ziyuan Gao AU - Christoph Ries AU - Hans Simon AU - Sandra Zilles BT - 29th Annual Conference on Learning Theory PY - 2016/06/06 DA - 2016/06/06 ED - Vitaly Feldman ED - Alexander Rakhlin ED - Ohad Shamir ID - pmlr-v49-gao16 PB - PMLR SP - 971 DP - PMLR EP - 997 L1 - http://proceedings.mlr.press/v49/gao16.pdf UR - http://proceedings.mlr.press/v49/gao16.html AB - We introduce a new model of teaching named “preference-based teaching” and a corresponding complexity parameter—the preference-based teaching dimension (PBTD)—representing the worst-case number of examples needed to teach any concept in a given concept class. Although the PBTD coincides with the well-known recursive teaching dimension (RTD) on finite classes, it is radically different on infinite ones: the RTD becomes infinite already for trivial infinite classes (such as half-intervals) whereas the PBTD evaluates to reasonably small values for a wide collection of infinite classes including classes consisting of so-called closed sets w.r.t. a given closure operator, including various classes related to linear sets over \mathbbN_0 (whose RTD had been studied quite recently) and including the class of Euclidean half-spaces (and some other geometric classes). On top of presenting these concrete results, we provide the reader with a theoretical framework (of a combinatorial flavor) which helps to derive bounds on the PBTD. ER -
APA
Gao, Z., Ries, C., Simon, H. & Zilles, S.. (2016). Preference-based Teaching. 29th Annual Conference on Learning Theory, in PMLR 49:971-997

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