Resetting a fixed broken ELBO

Abstract: Variational autoencoders (VAEs) are one class of generative probabilistic latent-variable models designed for inference based on known data. They balance reconstruction and regularizer terms. A variational approximation produces an evidence lower bound (ELBO). Multiplying the regularizer term by beta provides a beta-VAE/ELBO, improving disentanglement of the latent space. However, any beta value different than unity violates the laws of conditional probability. To provide a similarly-parameterized VAE, we develop a Renyi (versus Shannon) entropy VAE, and a variational approximation RELBO that introduces a similar parameter. The Renyi VAE has an additional Renyi regularizer-like term with a conditional distribution that is not learned. The term is evaluated essentially analytically using a Singular Value Decomposition method.