Update index.md

vae/index.md

@@ -56,7 +56,7 @@ From a generative modeling perspective, this model describes a generative proces
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-If one adopts the belief that the latent variables $$\bz$$ somehow encode semantically meaningful information about $$\bx$$, it is natural to view this generative process as first generating the "high-level" semantic information about $$\bx$$ first before fully generating $$\bx$$. Such a perspective motivates generative models with rich latent variable structures such as hierarchical generative models $$p(\bx, \bz_1, \ldots, \bz_m) = p(\bx \giv \bz_1)\prod_i p(\bz_i \giv \bz_{i+1})$$---where information about $$\bx$$ is generated hierarchically---and temporal models such as the Hidden Markov Model---where temporally-related high-level information is generated first before constructing $$\bx$$.
+If one adopts the belief that the latent variables $$\bz$$ somehow encode semantically meaningful information about $$\bx$$, it is natural to view this generative process as first generating the "high-level" semantic information about $$\bx$$ before fully generating $$\bx$$. Such a perspective motivates generative models with rich latent variable structures such as hierarchical generative models $$p(\bx, \bz_1, \ldots, \bz_m) = p(\bx \giv \bz_1)\prod_i p(\bz_i \giv \bz_{i+1})$$---where information about $$\bx$$ is generated hierarchically---and temporal models such as the Hidden Markov Model---where temporally-related high-level information is generated first before constructing $$\bx$$.
 
 We now consider a family of distributions $$\P_\bz$$ where $$p(\bz) \in \P_\bz$$ describes a probability distribution over $$\bz$$. Next, consider a family of conditional distributions $$\P_{\bx\giv \bz}$$ where $$p_\theta(\bx \giv \bz) \in \P_{\bx\giv \bz}$$ describes a conditional probability distribution over $$\bx$$ given $$\bz$$. Then our hypothesis class of generative models is the set of all possible combinations
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