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.

翻译：变分自编码器（VAEs）是一类基于已知数据进行推理的生成式概率潜变量模型。它们平衡了重建项和正则化项。变分近似产生证据下界（ELBO）。将正则化项乘以beta得到beta-VAE/ELBO，可改善潜空间的解缠性。然而，任何不等于1的beta值都会违反条件概率定律。为了提供参数化类似的VAE，我们开发了基于Rényi熵（而非香农熵）的VAE及其变分近似RELBO，引入类似参数。Rényi VAE具有一个额外的类似Rényi正则化的项，其条件分布无需学习，并通过奇异值分解方法进行基本解析评估。