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Novel Change of Measure Inequalities with Applications to PAC-Bayesian Bounds and Monte Carlo Estimation
Yuki Ohnishi, Jean Honorio · 2020-02-25 · via stat.ML updates on arXiv.org

We introduce several novel change of measure inequalities for two families of divergences: $f$-divergences and $α$-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 $α$-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.

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