Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 219 / 4 / b / i

Table of contents
- Solution i

Solution

For any approximating density

q_{ϕ}

,

lo g Z = E_{q_{ϕ}} lo g \frac{L ( θ ) π ( θ )}{q _{ϕ} ( θ )} + D_{KL} (q_{ϕ} ∥ p (θ ∣ y)) = ELBO (ϕ) + D_{KL} (q_{ϕ} ∥ p (θ ∣ y)) .

The evidence lower bound is therefore

ELBO (ϕ) = E_{q_{ϕ}} lo g L (θ) - D_{KL} (q_{ϕ} ∥ π) .

Since

lo g Z

does not depend on

ϕ

, maximizing the ELBO is equivalent to minimizing the divergence from

q_{ϕ}

to the posterior.

 Ancestors (11)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version