## The Neural Net Perspective

### Decoder

log-likelihood $\log p_{\phi}(x | z)$ 可以表示用 z 出重建 x 的有效程度。

## The Probability Model Perspective

KL 不易计算，因此 VI 优化 证据下界（ELBO） 来求解。

### ELBO

• Mean-field variational inference
• no shared parameters
• Amortized inference
• global parameters are shared across all datapoints

### Generative Network

where $\mu$ and $\sigma^{2}$ are deep networks with parameters $\beta$

### 步骤

• samples $\varepsilon_{i}$ for each data point and calculates $z_{i}$
• uses these samples to calculate noisy gradients with respect to $\nu$ and $\theta$
• follows those gradients in a stochastic optimization