论文标题
对VAE作为非线性缩放等距嵌入的定量理解
Quantitative Understanding of VAE as a Non-linearly Scaled Isometric Embedding
论文作者
论文摘要
变异自动编码器（VAE）估计与每个输入数据相对应的潜在变量的后验参数（均值和方差）。尽管它用于许多任务，但模型的透明度仍然是一个基本问题。本文通过VAE的差异几何学和信息理论解释对VAE性质进行了定量理解。根据速率延伸理论，最佳转换编码是通过使用PCA基础的正顺序变换来实现的，而转换空间是输入的等距。考虑到对VAE的转换编码的类比，我们在理论上和实验上阐明了VAE可以将VAE映射到隐式等距嵌入，其比例因子是从后验参数得出的。结果，我们可以从先前，损耗指标和相应的后验参数中估算输入空间中的数据概率，此外，可以像PCA的特征值一样评估每个潜在变量的定量重要性。
Variational autoencoder (VAE) estimates the posterior parameters (mean and variance) of latent variables corresponding to each input data. While it is used for many tasks, the transparency of the model is still an underlying issue. This paper provides a quantitative understanding of VAE property through the differential geometric and information-theoretic interpretations of VAE. According to the Rate-distortion theory, the optimal transform coding is achieved by using an orthonormal transform with PCA basis where the transform space is isometric to the input. Considering the analogy of transform coding to VAE, we clarify theoretically and experimentally that VAE can be mapped to an implicit isometric embedding with a scale factor derived from the posterior parameter. As a result, we can estimate the data probabilities in the input space from the prior, loss metrics, and corresponding posterior parameters, and further, the quantitative importance of each latent variable can be evaluated like the eigenvalue of PCA.
