2022年6月24日 · 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.

2022年10月1日 · Here is my question: how does maximizing ELBO lead to a good/correct posterior predictive distribution ...

2024年1月22日 · ELBO is a quantity used to approximate the log marginal likelihood of observed data, after applying ...

2019年10月25日 · 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.

2019年8月12日 · When using Bayesian optimisation in a neural network our loss function is equal to: Here the first term is the KL divergence between the approximate and true posteriors. The second term is the

2022年10月19日 · $\begingroup$ 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.

2020年10月18日 · Calculating ELBO in EM algorithm. Ask Question Asked 4 years, 5 months ago. Modified 4 years, 5 months ago.

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2020年2月12日 · 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.

2018年1月3日 · Technically ELBO would be a functional, a function that takes a function as an argument. However, in practice most problems assume some class of distributions (e.g. Gaussian, Gamma, etc), which eliminates the functional aspect of the problem and then optimize within this class of distributions, making the problem a single variable, or ...