# Questions tagged [variational-inference]

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### Do I need to take additional log det Jacobians for every PDF that uses the reparameterization trick?

Consider the - ELBO objective with reparameterization which is also used in VAE's:$$\mathcal L_{\theta,\phi}(x)=\log p_\theta(X|Z)+\log p_\theta(Z) +\log q_\phi(Z)$$ The reparameterization trick ...
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### How does Variational Autoencoder approximate the joint probability distribution?

I know that in Variational Inference the idea is to approximate the posterior P(z|x, y) and I know that Variational AutoEncoders (VAEs) use the idea of variational inference through neural network ...
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### How to measure posterior collapse if any

Is there any theoretical work on how to measure posterior collapse? One can measure decoder output, but it is not clear if the degradation (if any) happened due to posterior collapse or due to failing ...
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### Are there any methods that combine mcmc and VI?

Are there any methods that combine VI and MCMC? If it exists, why isn’t it used prominently over techniques such as NUTS or other VIs.
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### Why is the Wasserstein distance not used in Variational Inference

I just started learning the concept of variational inference in the context of variational Autoencoder, so please excuse me if the answer is obvious. I would like to know why traditionally, KL-...
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### Justification of the fixed variational distribution in diffusion models

Diffusion models can be regarded as latent variable models (Ho et al., 2020; Section 2), with the latents being an hierarchical chain of random variables $z_T → \dots → z_t → z_{t-1} → \dots → z_1$ (...
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### VAE : How is likelihood $p(x|z)$ defined?

Disclaimer : not a strong background in Bayesian statistics. I gather from questions such as this one and this one that in the context of VAEs, we suppose that we know the (form of the ?) prior $p(z)$ ...
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### why is VQ-VAE considered a variational encoder?

I'm reading about VQ-VAE and I'm not sure why do they say we can view it as a VAE. Can you explicitly show: what is the latent z-space - is it the discrete space where z can take the integers 1..K ...
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In VQ-VAE, we separate the codebook alignment loss $||sg(z_e(x))-e||^2$ and the commitment loss $||z_e(x)-sg(e)||^2$ where sg stands for the stop-gradient operator, and the loss is $||sg(z_e(x))-e||^2 ... • 3,350 4 votes 1 answer 141 views ### Why do we approximate the joint in ELBO if we already have access to it? I realized in variational inference, our goal is to approximate$p(z|x)$with$q(z)$. So we minimize$KL(q(z) || p(z|x)) = \mathbb{E}_{z \sim q} log\frac{q(z)}{p(z|x)}$. We then manipulate, through ... • 221 1 vote 1 answer 163 views ### Choice of approximate posterior in variational inference with positive support I have a simple probabilistic graphical model:$z \longrightarrow x$where$z_i \sim Exp\left(\lambda_i\right)$where subscript$i$denotes the$i$th dimension and$x|z \sim \mathcal{N}\left(f\left(z\...
I am trying to solve an inverse problem where I try to approximate a function $f(x)$ that fulfills the following equation \$\ddot{z}_m = \frac{\sigma^2}{2} \frac{\partial^2 f(z_m)}{\partial z^2} + \...