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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
maximum likelihood - ELBO - Jensen Inequality - Cross Validated 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 log can
In VAE, why use MSE loss between input x and decoded sample x from . . . In VAEs the conditional distribution p(x|z) p (x | z) is (usually) assumed to be a Gaussian distribution, i e p(x|z) = N(x;fdec(z),σ2I) p (x | z) = N (x; f d e c (z), σ 2 I) where σ2 σ 2 is a hyperparameter Hence the first term of ELBO, the logarithm of p(x|z) p (x | z), would be just a MSE loss between fdec(z) f d e c (z) and x x Other assumptions of p(x|z) p (x | z) can be used For
What is the relationship between VAE and EM algorithm? They are equivalent as ELBO We can say one goal of VAE is to push qϕ q ϕ and pθ(z|x) p θ (z | x) approaching each other asymptotically, and the part of θ θ of p p space which deal with Encoder are fixed after E-step And another goal is to educate the Decoder to generate samples as real as possible, which is M-step
Which exact loss do we minimize in a VAE model? 2 Answers Yes, maximizing the ELBO is equivalent to minimizing the negative ELBO This is a sign convention You minimize the negative ELBO (also called the variational free energy) in the standard training objective for a variational autoencoder
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
Is MSE loss a valid ELBO loss to measure? - Cross Validated 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
Why does Variational Inference work? - Cross Validated ELBO is a lower bound, and only matches the true likelihood when the q-distribution encoder we choose equals to the true posterior distribution Are there any guarantees that maximizing ELBO indeed