Variational autoencoders (VAEs) are one class of generative probabilistic latent-variable models designed for inference based on known data. We develop three variations on VAEs by introducing a second parameterized encoder/decoder pair and, for one variation, an additional fixed encoder. The parameters of the encoders/decoders are to be learned with a neural network. The fixed encoder is obtained by probabilistic-PCA. The variations are compared to the Evidence Lower Bound (ELBO) approximation to the original VAE. One variation leads to an Evidence Upper Bound (EUBO) that can be used in conjunction with the original ELBO to interrogate the convergence of the VAE.

翻译：变分自编码器是一类基于已知数据进行推断的生成式概率潜变量模型。我们通过引入第二个参数化编码器/解码器对，并针对其中一种变体额外引入一个固定编码器，提出了变分自编码器的三种变体。编码器/解码器的参数通过神经网络进行学习。其中固定编码器通过概率主成分分析获得。我们将这些变体与原始变分自编码器的证据下界近似进行了比较。其中一种变体产生了证据上界，该上界可与原始证据下界联合使用，以检验变分自编码器的收敛性。