Using Jensen's inequality, show that the Kullback-Leibler divergence between probability densities (f) and (g) is always positive;

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Using Jensen's inequality, show that the Kullback-Leibler divergence between probability densities $f$ and $g$ is always positive; that is,

\[ \mathbb{E} \ln \frac{f(\boldsymbol{X})}{g(\boldsymbol{X})} \geqslant 0 \]

where $\boldsymbol{X} \sim f$.

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Data Science And Machine Learning Mathematical And Statistical Methods

ISBN: 9781118710852

1st Edition

Authors: Dirk P. Kroese, Thomas Taimre, Radislav Vaisman, Zdravko Botev

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Question Posted: May 19, 2024 02:03 AM

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Using Jensen's inequality, show that the Kullback-Leibler divergence between probability densities (f) and (g) is always positive;

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Data Science And Machine Learning Mathematical And Statistical Methods

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