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Why isn't the evidence $p(x) = 1$ if it's an observed variable?

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A question on AI Stack Exchange asks why the evidence term p(x) is not equal to 1 when x is an observed variable in variational inference.

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“Every explanation of variational inference starts with the same basic premise: given an observed variable $x$ , and a latent variable $z$ , $$ p(z|x)=\frac{p(x,z)}{p(x)} $$ and then proceeds to expand $p(x)$ as an expectation over $z$ : $$ p(x) =…”
AI Stack Exchange, 13 Sept 2026, 01:09.

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