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- Understanding the Evidence Lower Bound (ELBO) - Cross Validated
With that in mind, the ELBO can be a meaningful lower bound on the log-likelihood: both are negative, but ELBO is lower How much lower? The KL divergence from the conditional distribution I don’t see where you think the figure is indicating that it should be positive The bottom of the diagram isn’t 0
- How does maximizing ELBO in Bayesian neural networks give us the . . .
Here is my question: how does maximizing ELBO lead to a good correct posterior predictive distribution
- maximum likelihood - ELBO - Jensen Inequality - Cross Validated
ELBO is a quantity used to approximate the log marginal likelihood of observed data, after applying
- maximum likelihood - VQ-VAE objective - is it ELBO maximization, or . . .
$\begingroup$ thanks! so if the ELBO itself is tractable - why does rocca show that we are optimizing the KL divergence? he shows that we can develop the KL divergence between the approximate posterior and the true posterior (which is indeed unknown) as a sum of the data likelihood and the KL divergence between the approximate posterior and the prior, and then proceeds to optimize that
- Gradients of KL divergence and ELBO for variational inference
The ELBO $\mathcal{L}(\phi)$ can be written as the difference between the log evidence and the KL divergence between the variational distribution and true posterior: $$\mathcal{L}(\phi) = \log p(x) - D_{KL} \Big( q_\phi(\theta) \parallel p(\theta \mid x) \Big)$$ Take the gradient of both sides w r t the variational parameters
- Which exact loss do we minimize in a VAE model?
Since our objective is to minimize the ELBO (to bring our approximate posterior as close as possible to the true one) and the evidence is independent of q (correctly noted independent of the parameters of q, if we are taking a parametric approximation for q), minimizing this KL divergence leads to maximizing the ELBO
- neural networks - ELBO maximization with SGD - Cross Validated
Maximizing the ELBO, however, does have analytical update formulas (i e formulas for the E and M steps) I understand why in this case maximizing the ELBO is a useful approximation However, in more complex models, such as VAE, the E M steps themselves don't have a closed solution, and ELBO maximization is done with SGD
- Variational Inference: Computation of ELBO and CAVI algorithm
I am reading studying this paper 1 and got confused with some expressions It might be basic for many of you, so my apologizes In the paper the following prior model is assumed: $\\mu_k \\sim \\mat
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