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If the probability measures $P$ and $Q$ are mutually absolutely continuous, Kullback divergence $K(P,Q)=\int \log\left(\frac{\mathrm{d}P}{\mathrm{d}Q}\right)\mathrm{d}P$, and chi-square divergence $ \chi^2(Q,P) = \int \left( \frac{\mathrm{d}Q}{\mathrm{d}P}−1\right)^2 \mathrm{d}P$, how to prove that

$$ K(P,Q) \leqslant \frac{1}{2}\chi^2(Q,P)$$

  • 2
    What did you try? Which similar problems can you solve?2012-04-26
  • 0
    If you remove the 1/2 factor, then the inequality holds (assuming log means natural log).2017-12-20

1 Answers 1