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Bookmark or Share- Gradients of KL divergence and ELBO for variational inference4. 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. Assuming that we can compute gradients of KLD, my question is the following: are gradients of ELBO and KLD evaluated at the same ...
- Is MSE loss a valid ELBO loss to measure? - Cross ValidatedYes, MSE is a valid ELBO loss; it's one of the examples used in the paper. the authors write. We let pθ(x|z) p θ (x | z) be a multivariate Gaussian (in case of real-valued data) or Bernoulli (in case of binary data) whose distribution parameters are computed from z z with a MLP (a fully-connected neural network with a single hidden layer, see ...
- Why is computing $\\log p(x)$ difficult, but not the ELBO?This looks quite similar to how we would compute the evidence lower bound (ELBO), which is used to approximate the marginal log-likelihood by introducing a variational distribution q(z; x): logp(x) ≥ ELBO(x) = ∫dzq(z; x)[logp(x | z)p(z) − logq(z; x)] The ELBO is usually approximated using multiple samples from q: ELBO(x) ≈ logp(x | zi)p ...
- Understanding the Evidence Lower Bound (ELBO) - Cross ValidatedLook at the following equation: KL(q(z)‖P(z ∣ x, θ)) = logP(x ∣ θ) − L(q, θ) Looking at it this way, the KL is broken down into two pieces, the likelihood and the ELBO. If you are looking to find the q which maximizes this lowerbound for a fixed θ, maximizing the ELBO by finding the optimal q will necessarily only make the KL term ...
- Calculating ELBO in EM algorithm - Cross ValidatedCalculating ELBO in EM algorithm. In Andrew Ng's CS229 notes, a nice derivation of EM algorithm is given. With some minor notation modifications, the algorithm is written as follows: E-step: For each i, Qi(zi) = p(zi | xi, θold) M-step: θ = arg maxθ ∑Ni = 1ELBO(xi; Qi, θ) = arg maxθ ∑Ni = 1 ∑ziQi(zi)logp (xi zi, θ) p (zi θ) Qi (zi ...
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