# 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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### What is the meaning of log p(x) in VAE math and why is it constant

I was reading the article on medium, where the author cites this equation for Variational Inference: \begin{align*} \text{KL}(q(z|x^{(i)})||p(z|x^{(i)})) &= \int_z q(z|x^{(i)})\text{log}\frac{q(z|...
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### How does using the ELBO in VAEs make the problem tractable?

I'm studying Variational Autoencoders and a lot of the literature says that the posterior is intractable because the marginal distribution p(x) is intractable since the space of z is so large we ...
1 vote
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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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### Trouble understanding Variational Inference objective

I was reading the Meta Temporal Point Processes paper and was having trouble understading the training objective presented. The authors state that it is the ELBO used in Variational Inference ...
### 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 \$...