General Oracle Inequalities for Gibbs Posterior with Application to Ranking

Cheng Li, Wenxin Jiang, Martin Tanner
Proceedings of the 26th Annual Conference on Learning Theory, PMLR 30:512-521, 2013.

Abstract

In this paper, we summarize some recent results in Li et al. (2012), which can be used to extend an important PAC-Bayesian approach, namely the Gibbs posterior, to study the nonadditive ranking risk. The methodology is based on assumption-free risk bounds and nonasymptotic oracle inequalities, which leads to nearly optimal convergence rates and optimal model selection to balance the approximation errors and the stochastic errors.

Cite this Paper

BibTeX
@InProceedings{pmlr-v30-Li13, title = {General Oracle Inequalities for Gibbs Posterior with Application to Ranking}, author = {Li, Cheng and Jiang, Wenxin and Tanner, Martin}, booktitle = {Proceedings of the 26th Annual Conference on Learning Theory}, pages = {512--521}, year = {2013}, editor = {Shalev-Shwartz, Shai and Steinwart, Ingo}, volume = {30}, series = {Proceedings of Machine Learning Research}, address = {Princeton, NJ, USA}, month = {12--14 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v30/Li13.pdf}, url = {https://proceedings.mlr.press/v30/Li13.html}, abstract = {In this paper, we summarize some recent results in Li et al. (2012), which can be used to extend an important PAC-Bayesian approach, namely the Gibbs posterior, to study the nonadditive ranking risk. The methodology is based on assumption-free risk bounds and nonasymptotic oracle inequalities, which leads to nearly optimal convergence rates and optimal model selection to balance the approximation errors and the stochastic errors.} }
Endnote
%0 Conference Paper %T General Oracle Inequalities for Gibbs Posterior with Application to Ranking %A Cheng Li %A Wenxin Jiang %A Martin Tanner %B Proceedings of the 26th Annual Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2013 %E Shai Shalev-Shwartz %E Ingo Steinwart %F pmlr-v30-Li13 %I PMLR %P 512--521 %U https://proceedings.mlr.press/v30/Li13.html %V 30 %X In this paper, we summarize some recent results in Li et al. (2012), which can be used to extend an important PAC-Bayesian approach, namely the Gibbs posterior, to study the nonadditive ranking risk. The methodology is based on assumption-free risk bounds and nonasymptotic oracle inequalities, which leads to nearly optimal convergence rates and optimal model selection to balance the approximation errors and the stochastic errors.
RIS
TY - CPAPER TI - General Oracle Inequalities for Gibbs Posterior with Application to Ranking AU - Cheng Li AU - Wenxin Jiang AU - Martin Tanner BT - Proceedings of the 26th Annual Conference on Learning Theory DA - 2013/06/13 ED - Shai Shalev-Shwartz ED - Ingo Steinwart ID - pmlr-v30-Li13 PB - PMLR DP - Proceedings of Machine Learning Research VL - 30 SP - 512 EP - 521 L1 - http://proceedings.mlr.press/v30/Li13.pdf UR - https://proceedings.mlr.press/v30/Li13.html AB - In this paper, we summarize some recent results in Li et al. (2012), which can be used to extend an important PAC-Bayesian approach, namely the Gibbs posterior, to study the nonadditive ranking risk. The methodology is based on assumption-free risk bounds and nonasymptotic oracle inequalities, which leads to nearly optimal convergence rates and optimal model selection to balance the approximation errors and the stochastic errors. ER -
APA
Li, C., Jiang, W. & Tanner, M.. (2013). General Oracle Inequalities for Gibbs Posterior with Application to Ranking. Proceedings of the 26th Annual Conference on Learning Theory, in Proceedings of Machine Learning Research 30:512-521 Available from https://proceedings.mlr.press/v30/Li13.html.

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