Tight Bounds on Proper Equivalence Query Learning of DNF

Lisa Hellerstein, Devorah Kletenik, Linda Sellie, Rocco Servedio
Proceedings of the 25th Annual Conference on Learning Theory, PMLR 23:31.1-31.18, 2012.

Abstract

We prove a new structural lemma for partial Boolean functions \emphf, which we call the \emphseed lemma for \emphDNF. Using the lemma, we give the first subexponential algorithm for proper learning of poly(\emphn)-term DNF in Angluin’s Equivalence Query (EQ) model. The algorithm has time and query complexity 2^(Õ√\emphn), which is optimal. We also give a new result on certificates for DNF-size, a simple algorithm for properly PAC-learning DNF, and new results on EQ-learning log \emphn-term DNF and decision trees.

Cite this Paper

BibTeX
@InProceedings{pmlr-v23-hellerstein12, title = {Tight Bounds on Proper Equivalence Query Learning of DNF}, author = {Hellerstein, Lisa and Kletenik, Devorah and Sellie, Linda and Servedio, Rocco}, booktitle = {Proceedings of the 25th Annual Conference on Learning Theory}, pages = {31.1--31.18}, year = {2012}, editor = {Mannor, Shie and Srebro, Nathan and Williamson, Robert C.}, volume = {23}, series = {Proceedings of Machine Learning Research}, address = {Edinburgh, Scotland}, month = {25--27 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v23/hellerstein12/hellerstein12.pdf}, url = {https://proceedings.mlr.press/v23/hellerstein12.html}, abstract = {We prove a new structural lemma for partial Boolean functions \emphf, which we call the \emphseed lemma for \emphDNF. Using the lemma, we give the first subexponential algorithm for proper learning of poly(\emphn)-term DNF in Angluin’s Equivalence Query (EQ) model. The algorithm has time and query complexity 2^(Õ√\emphn), which is optimal. We also give a new result on certificates for DNF-size, a simple algorithm for properly PAC-learning DNF, and new results on EQ-learning log \emphn-term DNF and decision trees.} }
Endnote
%0 Conference Paper %T Tight Bounds on Proper Equivalence Query Learning of DNF %A Lisa Hellerstein %A Devorah Kletenik %A Linda Sellie %A Rocco Servedio %B Proceedings of the 25th Annual Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2012 %E Shie Mannor %E Nathan Srebro %E Robert C. Williamson %F pmlr-v23-hellerstein12 %I PMLR %P 31.1--31.18 %U https://proceedings.mlr.press/v23/hellerstein12.html %V 23 %X We prove a new structural lemma for partial Boolean functions \emphf, which we call the \emphseed lemma for \emphDNF. Using the lemma, we give the first subexponential algorithm for proper learning of poly(\emphn)-term DNF in Angluin’s Equivalence Query (EQ) model. The algorithm has time and query complexity 2^(Õ√\emphn), which is optimal. We also give a new result on certificates for DNF-size, a simple algorithm for properly PAC-learning DNF, and new results on EQ-learning log \emphn-term DNF and decision trees.
RIS
TY - CPAPER TI - Tight Bounds on Proper Equivalence Query Learning of DNF AU - Lisa Hellerstein AU - Devorah Kletenik AU - Linda Sellie AU - Rocco Servedio BT - Proceedings of the 25th Annual Conference on Learning Theory DA - 2012/06/16 ED - Shie Mannor ED - Nathan Srebro ED - Robert C. Williamson ID - pmlr-v23-hellerstein12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 23 SP - 31.1 EP - 31.18 L1 - http://proceedings.mlr.press/v23/hellerstein12/hellerstein12.pdf UR - https://proceedings.mlr.press/v23/hellerstein12.html AB - We prove a new structural lemma for partial Boolean functions \emphf, which we call the \emphseed lemma for \emphDNF. Using the lemma, we give the first subexponential algorithm for proper learning of poly(\emphn)-term DNF in Angluin’s Equivalence Query (EQ) model. The algorithm has time and query complexity 2^(Õ√\emphn), which is optimal. We also give a new result on certificates for DNF-size, a simple algorithm for properly PAC-learning DNF, and new results on EQ-learning log \emphn-term DNF and decision trees. ER -
APA
Hellerstein, L., Kletenik, D., Sellie, L. & Servedio, R.. (2012). Tight Bounds on Proper Equivalence Query Learning of DNF. Proceedings of the 25th Annual Conference on Learning Theory, in Proceedings of Machine Learning Research 23:31.1-31.18 Available from https://proceedings.mlr.press/v23/hellerstein12.html.

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