Automatic Differentiation Variational Inference (ADVI) is a useful tool for efficiently learning probabilistic models in machine learning. Generally approximate posteriors learned by ADVI are forced to be unimodal in order to facilitate use of the reparameterization trick. In this paper, we show how stratified sampling may be used to enable mixture distributions as the approximate posterior, and derive a new lower bound on the evidence analogous to the importance weighted autoencoder (IWAE). We show that this ``SIWAE'' is a tighter bound than both IWAE and the traditional ELBO, both of which are special instances of this bound. We verify empirically that the traditional ELBO objective disfavors the presence of multimodal posterior distributions and may therefore not be able to fully capture structure in the latent space. Our experiments show that using the SIWAE objective allows the encoder to learn more complex distributions which regularly contain multimodality, resulting in higher accuracy and better calibration in the presence of incomplete, limited, or corrupted data.

本论文引入了分层抽样的方法，实现了对混合分布的自动微分变分推断（ADVI）； 并且通过建立重要性加权自编码器（IWAE）类似的较紧下界，进一步验证了该方法相较于传统ELBO或IWAE的优势，特别是在latents变量中有多峰分布时，表现出更高的准确性和更好的校准性。

混合自动微分变分推断