2022年6月24日 · The Evidence Lower Bound (ELBO) is a key concept in variational inference, helping to approximate complex probability distributions.

2022年10月1日 · In particular the ELBO doesn't feature the true posterior p(w | D) as you don't know it (if you did you wouldn't be trying to approximate it). The dropped term leading to the inequality "gap" (leading to a lower bound), is the KL divergence between the approximate and true posterior, which is (implicitly) minimised as the ELBO is maximised.

2024年1月22日 · ELBO is a quantity used to approximate the log marginal likelihood of observed data, after applying Jensen's inequality to the log likelihood leading to the fact that maximizing the ELBO with respect to the parameters of p p is equivalent to minimizing the KL-divergence from pθ(⋅|x) p θ (⋅ | x) to qϕ(⋅|x) q ϕ (⋅ | x). Without this approximation, sampling before taking the …

2022年10月19日 · 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 ...

2019年10月25日 · When doing variational inference, due to intractability we typically maximize the evidence lower bound (ELBO) instead of minimizing Kullback-Leibler divergence (KLD) between our approximate and exact posterior.

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2019年8月12日 · If we maximise the ELBO, will our neural network estimate have the same variance as the logistic regression model? Is there a way we can proof what the asymptotic properties of the neural network estimations will be?

2018年10月2日 · 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...

2022年6月30日 · The Kingma et al. paper is very readable, and a good place to start understanding how and why VAEs work. Kingma, Diederik P., and Max Welling. "Auto-encoding variational Bayes." arXiv preprint arXiv:1312.6114 (2013). "Another example used MSE loss (as follow), is MSE loss a valid ELBO loss to measure p (x|z)?" Yes, MSE is a valid ELBO loss; it's one of the examples used in the paper. the ...

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.