2023-11-29

Elbo

The formula for the ELBO in the context of the Variational Autoencoder is given by the following: $$ \operatorname{ELBO}[\boldsymbol{\theta}, \boldsymbol{\phi}]=\int q(\mathbf{z} \mid \mathbf{x}, \boldsymbol{\theta}) \log [\operatorname{Pr}(\mathbf{x} \mid \mathbf{z}, \boldsymbol{\phi})] d \mathbf{z}-\mathrm{D}_{K L}[q(\mathbf{z} \mid \mathbf{x}, \boldsymbol{\theta}) | \operatorname{Pr}(\mathbf{z})] \text {, } $$