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[typo err] lower bound fomula mistake in 'Deep Generative Model.ipynb'

Open jjongjjong opened this issue 5 years ago • 0 comments

before

\begin{align}
\log p(x) &= \log \sum_{y} \int q(z,y|x) \frac{p(x, y, z)}{q(z,y|x)} \ dz \geq \sum_{y} q(y|x) \int q(z|x, y) \log \frac{p(x, y, z)}{q(z,y|x)} \ dz\\
&= \sum_{y} q(y|x) \int q(z|x, y) \log \frac{p(x, y, z)}{q(z,y|x)} \ dz + \sum_{y} q(y|x) \log q(y|x) \int q(z|x, y) \ dz\\
&= \sum_{y} q(y|x) (- \mathcal{L}(x,y)) + \mathcal{H}(q(y|x)) = - \mathcal{U}(x)
\end{align}

after

\begin{align}
\log p(x) &= \log \sum_{y} \int q(z,y|x) \frac{p(x, y, z)}{q(z,y|x)} \ dz \geq \sum_{y} q(y|x) \int q(z|x, y) \log \frac{p(x, y, z)}{q(z,y|x)} \ dz\\
&= \sum_{y} q(y|x) \int q(z|x, y) \log \frac{p(x, y, z)}{q(z,y|x)} \ dz + \sum_{y} q(y|x) \log q(y|x) \int q(z|x, y) \ dz\\
&= \sum_{y} q(y|x) (- \mathcal{L}(x,y)) + \mathcal{H}(q(y|x)) = - \mathcal{U}(x)
\end{align}

jjongjjong avatar Apr 16 '20 02:04 jjongjjong