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fix typos
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figures/coupling-layer-backward.svg

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slides/amortized-inference.qmd

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@@ -75,7 +75,7 @@ $$
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\begin{aligned}
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\hat{\phi}, \hat{\psi} = \operatorname*{argmin}_{\phi, \psi} & \mathbb{E}_{x \sim p(x)} \mathbb{KL}\big[p(\theta \mid x) || q_\phi(\theta \mid h_\psi(x))\big] = \\
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= \operatorname*{argmin}_{\phi, \psi} & \mathbb{E}_{x \sim p(x)} \mathbb{E}_{\theta \sim p(\theta \mid x)} \log \frac{p(\theta \mid x)}{q_\phi(\theta \mid h_\psi(x))} \propto \\
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\propto \operatorname*{argmin}_{\phi, \psi} & - \mathbb{E}_{(x, \theta) \sim p(x, \theta)} q_\phi(\theta \mid h_\psi(x)) \approx\\
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\propto \operatorname*{argmin}_{\phi, \psi} & - \mathbb{E}_{(x, \theta) \sim p(x, \theta)} \log q_\phi(\theta \mid h_\psi(x)) \approx\\
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\approx \operatorname*{argmin}_{\phi, \psi} & - \frac{1}{S}\sum_{s=1}^S \log q_\phi(\theta^{(s)} \mid h_\psi(x^{(s)}))
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\end{aligned}
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$$

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