Novel Change of Measure Inequalities with Applications to PAC-Bayesian Bounds and Monte Carlo Estimation

@InProceedings{pmlr-v130-ohnishi21a,
  title = 	 { Novel Change of Measure Inequalities with Applications to PAC-Bayesian Bounds  and Monte Carlo Estimation },
  author =       {Ohnishi, Yuki and Honorio, Jean},
  booktitle = 	 {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics},
  pages = 	 {1711--1719},
  year = 	 {2021},
  editor = 	 {Banerjee, Arindam and Fukumizu, Kenji},
  volume = 	 {130},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {13--15 Apr},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v130/ohnishi21a/ohnishi21a.pdf},
  url = 	 {https://proceedings.mlr.press/v130/ohnishi21a.html},
  abstract = 	 { We introduce several novel change of measure inequalities for two families of divergences: $f$-divergences and $\alpha$-divergences. We show how the variational representation for $f$-divergences leads to novel change of measure inequalities. We also present a multiplicative change of measure inequality for $\alpha$-divergences and a generalized version of Hammersley-Chapman-Robbins inequality. Finally, we present several applications of our change of measure inequalities, including PAC-Bayesian bounds for various classes of losses and non-asymptotic intervals for Monte Carlo estimates. }
}