General Oracle Inequalities for Gibbs Posterior with Application to Ranking
; Proceedings of the 26th Annual Conference on Learning Theory, PMLR 30:512-521, 2013.
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.