A Unified Algorithmic Approach for Efficient Online Label Ranking

Shai Shalev-Shwartz, Yoram Singer
; Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2:452-459, 2007.

Abstract

Label ranking is the task of ordering labels with respect to their relevance to an input instance. We describe a unified approach for the online label ranking task. We do so by casting the online learning problem as a game against a competitor who receives all the examples in advance and sets its label ranker to be the optimal solution of a constrained optimization problem. This optimization problem consists of two terms: the empirical label-ranking loss of the competitor and a complexity measure of the competitor’s ranking function. We then describe and analyze a framework for online label ranking that incrementally ascends the dual problem corresponding to the competitor’s optimization problem. The generality of our framework enables us to derive new online update schemes. In particular, we use the relative entropy as a complexity measure to derive efficient multiplicative algorithms for the label ranking task. Depending on the specific form of the instances, the multiplicative updates either have a closed form or can be calculated very efficiently by tailoring an interior point procedure to the label ranking task. We demonstrate the potential of our approach in a few experiments with email categorization tasks.

Cite this Paper


BibTeX
@InProceedings{pmlr-v2-shalev-shwartz07a, title = {A Unified Algorithmic Approach for Efficient Online Label Ranking}, author = {Shai Shalev-Shwartz and Yoram Singer}, booktitle = {Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics}, pages = {452--459}, year = {2007}, editor = {Marina Meila and Xiaotong Shen}, volume = {2}, series = {Proceedings of Machine Learning Research}, address = {San Juan, Puerto Rico}, month = {21--24 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v2/shalev-shwartz07a/shalev-shwartz07a.pdf}, url = {http://proceedings.mlr.press/v2/shalev-shwartz07a.html}, abstract = {Label ranking is the task of ordering labels with respect to their relevance to an input instance. We describe a unified approach for the online label ranking task. We do so by casting the online learning problem as a game against a competitor who receives all the examples in advance and sets its label ranker to be the optimal solution of a constrained optimization problem. This optimization problem consists of two terms: the empirical label-ranking loss of the competitor and a complexity measure of the competitor’s ranking function. We then describe and analyze a framework for online label ranking that incrementally ascends the dual problem corresponding to the competitor’s optimization problem. The generality of our framework enables us to derive new online update schemes. In particular, we use the relative entropy as a complexity measure to derive efficient multiplicative algorithms for the label ranking task. Depending on the specific form of the instances, the multiplicative updates either have a closed form or can be calculated very efficiently by tailoring an interior point procedure to the label ranking task. We demonstrate the potential of our approach in a few experiments with email categorization tasks.} }
Endnote
%0 Conference Paper %T A Unified Algorithmic Approach for Efficient Online Label Ranking %A Shai Shalev-Shwartz %A Yoram Singer %B Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2007 %E Marina Meila %E Xiaotong Shen %F pmlr-v2-shalev-shwartz07a %I PMLR %J Proceedings of Machine Learning Research %P 452--459 %U http://proceedings.mlr.press %V 2 %W PMLR %X Label ranking is the task of ordering labels with respect to their relevance to an input instance. We describe a unified approach for the online label ranking task. We do so by casting the online learning problem as a game against a competitor who receives all the examples in advance and sets its label ranker to be the optimal solution of a constrained optimization problem. This optimization problem consists of two terms: the empirical label-ranking loss of the competitor and a complexity measure of the competitor’s ranking function. We then describe and analyze a framework for online label ranking that incrementally ascends the dual problem corresponding to the competitor’s optimization problem. The generality of our framework enables us to derive new online update schemes. In particular, we use the relative entropy as a complexity measure to derive efficient multiplicative algorithms for the label ranking task. Depending on the specific form of the instances, the multiplicative updates either have a closed form or can be calculated very efficiently by tailoring an interior point procedure to the label ranking task. We demonstrate the potential of our approach in a few experiments with email categorization tasks.
RIS
TY - CPAPER TI - A Unified Algorithmic Approach for Efficient Online Label Ranking AU - Shai Shalev-Shwartz AU - Yoram Singer BT - Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics PY - 2007/03/11 DA - 2007/03/11 ED - Marina Meila ED - Xiaotong Shen ID - pmlr-v2-shalev-shwartz07a PB - PMLR SP - 452 DP - PMLR EP - 459 L1 - http://proceedings.mlr.press/v2/shalev-shwartz07a/shalev-shwartz07a.pdf UR - http://proceedings.mlr.press/v2/shalev-shwartz07a.html AB - Label ranking is the task of ordering labels with respect to their relevance to an input instance. We describe a unified approach for the online label ranking task. We do so by casting the online learning problem as a game against a competitor who receives all the examples in advance and sets its label ranker to be the optimal solution of a constrained optimization problem. This optimization problem consists of two terms: the empirical label-ranking loss of the competitor and a complexity measure of the competitor’s ranking function. We then describe and analyze a framework for online label ranking that incrementally ascends the dual problem corresponding to the competitor’s optimization problem. The generality of our framework enables us to derive new online update schemes. In particular, we use the relative entropy as a complexity measure to derive efficient multiplicative algorithms for the label ranking task. Depending on the specific form of the instances, the multiplicative updates either have a closed form or can be calculated very efficiently by tailoring an interior point procedure to the label ranking task. We demonstrate the potential of our approach in a few experiments with email categorization tasks. ER -
APA
Shalev-Shwartz, S. & Singer, Y.. (2007). A Unified Algorithmic Approach for Efficient Online Label Ranking. Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, in PMLR 2:452-459

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