Monte Carlo Estimation

Definition

Monte Carlo estimation approximates an expectation by averaging over random samples. For example,

$$\mathbb E_{z\sim q_\phi}[f(z)] \approx \frac{1}{m}\sum_{i=1}^m f(z^{(i)}), \quad z^{(i)}\sim q_\phi.$$

Why it matters in Q1

The ELBO is estimated using samples from the variational distribution.