22
0
v1v2 (latest)

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

Abstract

We introduce several novel change of measure inequalities for two families of divergences: ff-divergences and α\alpha-divergences. We show how the variational representation for ff-divergences leads to novel change of measure inequalities. We also present a multiplicative change of measure inequality for α\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.

View on arXiv
Comments on this paper