New Bounds for Learning Intervals with Implications for Semi-Supervised Learning

David P. Helmbold, Philip M. Long
Proceedings of the 25th Annual Conference on Learning Theory, PMLR 23:30.1-30.15, 2012.

Abstract

We study learning of initial intervals in the prediction model. We show that for each distribution \emphD over the domain, there is an algorithm \emphA_D, whose probability of a mistake in round m is at most \emph(½ + o(1))/m. We also show that the best possible bound that can be achieved in the case in which the same algorithm \emphA must be applied for all distributions \emphD is at least (^1⁄_√\emphe - o(1))^1⁄_\emphm > (^3⁄_5-o(1))^1⁄_\emphm. Informally, “knowing” the distribution \emphD enables an algorithm to reduce its error rate by a constant factor strictly greater than 1. As advocated by Ben-David et al. (2008), knowledge of \emphD can be viewed as an idealized proxy for a large number of unlabeled examples.

Cite this Paper

BibTeX
@InProceedings{pmlr-v23-helmbold12, title = {New Bounds for Learning Intervals with Implications for Semi-Supervised Learning}, author = {Helmbold, David P. and Long, Philip M.}, booktitle = {Proceedings of the 25th Annual Conference on Learning Theory}, pages = {30.1--30.15}, 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/helmbold12/helmbold12.pdf}, url = {https://proceedings.mlr.press/v23/helmbold12.html}, abstract = {We study learning of initial intervals in the prediction model. We show that for each distribution \emphD over the domain, there is an algorithm \emphA_D, whose probability of a mistake in round m is at most \emph(½ + o(1))/m. We also show that the best possible bound that can be achieved in the case in which the same algorithm \emphA must be applied for all distributions \emphD is at least (^1⁄_√\emphe - o(1))^1⁄_\emphm > (^3⁄_5-o(1))^1⁄_\emphm. Informally, “knowing” the distribution \emphD enables an algorithm to reduce its error rate by a constant factor strictly greater than 1. As advocated by Ben-David et al. (2008), knowledge of \emphD can be viewed as an idealized proxy for a large number of unlabeled examples.} }
Endnote
%0 Conference Paper %T New Bounds for Learning Intervals with Implications for Semi-Supervised Learning %A David P. Helmbold %A Philip M. Long %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-helmbold12 %I PMLR %P 30.1--30.15 %U https://proceedings.mlr.press/v23/helmbold12.html %V 23 %X We study learning of initial intervals in the prediction model. We show that for each distribution \emphD over the domain, there is an algorithm \emphA_D, whose probability of a mistake in round m is at most \emph(½ + o(1))/m. We also show that the best possible bound that can be achieved in the case in which the same algorithm \emphA must be applied for all distributions \emphD is at least (^1⁄_√\emphe - o(1))^1⁄_\emphm > (^3⁄_5-o(1))^1⁄_\emphm. Informally, “knowing” the distribution \emphD enables an algorithm to reduce its error rate by a constant factor strictly greater than 1. As advocated by Ben-David et al. (2008), knowledge of \emphD can be viewed as an idealized proxy for a large number of unlabeled examples.
RIS
TY - CPAPER TI - New Bounds for Learning Intervals with Implications for Semi-Supervised Learning AU - David P. Helmbold AU - Philip M. Long 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-helmbold12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 23 SP - 30.1 EP - 30.15 L1 - http://proceedings.mlr.press/v23/helmbold12/helmbold12.pdf UR - https://proceedings.mlr.press/v23/helmbold12.html AB - We study learning of initial intervals in the prediction model. We show that for each distribution \emphD over the domain, there is an algorithm \emphA_D, whose probability of a mistake in round m is at most \emph(½ + o(1))/m. We also show that the best possible bound that can be achieved in the case in which the same algorithm \emphA must be applied for all distributions \emphD is at least (^1⁄_√\emphe - o(1))^1⁄_\emphm > (^3⁄_5-o(1))^1⁄_\emphm. Informally, “knowing” the distribution \emphD enables an algorithm to reduce its error rate by a constant factor strictly greater than 1. As advocated by Ben-David et al. (2008), knowledge of \emphD can be viewed as an idealized proxy for a large number of unlabeled examples. ER -
APA
Helmbold, D.P. & Long, P.M.. (2012). New Bounds for Learning Intervals with Implications for Semi-Supervised Learning. Proceedings of the 25th Annual Conference on Learning Theory, in Proceedings of Machine Learning Research 23:30.1-30.15 Available from https://proceedings.mlr.press/v23/helmbold12.html.

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