We provide theoretical and empirical evidence that using tighter evidence
lower bounds (ELBOs) can be detrimental to the process of learning an inference
network by reducing the signal-to-noise ratio of the gradient estimator. Our
results call into question common implicit assumptions that tighter ELBOs are
better variational objectives for simultaneous model learning and inference
amortization schemes. Based on our insights, we introduce three new algorithms:
the partially importance weighted auto-encoder (PIWAE), the multiply importance
weighted auto-encoder (MIWAE), and the combination importance weighted
auto-encoder (CIWAE), each of which includes the standard importance weighted
auto-encoder (IWAE) as a special case. We show that each can deliver
improvements over IWAE, even when performance is measured by the IWAE target
itself. Furthermore, our results suggest that PIWAE may be able to deliver
simultaneous improvements in the training of both the inference and generative
networks.

本文提供理论和实证证据表明，使用更严格的证据下界（ELBO）可能会降低梯度估计器的信噪比，从而对学习推理网络产生不利影响，并介绍了三种新算法：偏重要性加权自动编码器（PIWAE），乘法重要性加权自动编码器（MIWAE）和组合重要性加权自动编码器（CIWAE）。同时，我们的结果表明，PIWAE 可以同时改善推理和生成网络的训练。