# Questions tagged [variational-inference]

For questions related to variational inference (VI), an optimization-based approach to the inference problem (i.e. the computation of the posterior given the prior, likelihood, and marginal). VI is used, for example, in the context of auto-encoders (VAEs) and Bayesian neural networks (BNNs).

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### Why do we use $q_{\phi}(z \mid x^{(i)})$ in the objective function of amortized variational inference, while sometimes we use $q(z)$?

In page 21 here, it states: General Idea of Amortization: if same inference problem needs to be solved many times, can we parameterize a neural network to solve it? Our case: for all $x^{(i)}$ we ...
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### What is $p(Z)$ and what happens to the variational posterior $q(Z;X)$ during data synthesis (after training)?

From my understanding of inference problems, we want to compute the posterior $p(Z|X=D)$, for some observed dataset $D=(x^1, x^2,\dots,x^n)$ of $n$ independent observations, in order to "update&...
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### what's the best way of Inferring probability chance of heads with a coin of Unknown Bias that changes regularly

hi what would be the best strategy to infer the range of probabilities of getting heads with a coin of Unknown Bias that is variable? I'm working on a similar problem with a game AI. I'm working on a ...
### Why isn't the evidence $p(x) = 1$ if it's an observed variable?
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 \$...