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2013 COLT COLT 2013

General Oracle Inequalities for Gibbs Posterior with Application to Ranking

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.

📈 Trend Setter - Supervised Learning
🧭 Keyword Pioneer - gibbs posterior
🐝 Cross-Pollinator - Artificial Intelligence, Computer Vision, Data Science & Analytics, Deep Learning, Interdisciplinary, Knowledge & Reasoning, Machine Learning, Mathematics & Optimization, Natural Language Processing, Reinforcement Learning
🐣 Hot Topic Early Bird - model selection

Authors

Cheng Li , Wenxin Jiang , Martin Tanner

Topics

Machine Learning > Optimization & Theory > Bayesian Inference Machine Learning > Optimization & Theory > Learning Theory Machine Learning > Bayesian & Probabilistic > Bayesian Learning Machine Learning > Learning Types > Supervised Learning Machine Learning > Core Methods > Ranking

Keywords

model selection oracle inequalities oracle inequality pac-bayesian bound convergence rate gibbs posterior ranking risk
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