Tighter Variational Bounds are Not Necessarily Better
This work addresses a fundamental issue in variational inference for machine learning practitioners, offering incremental algorithmic improvements.
The paper challenges the assumption that tighter evidence lower bounds (ELBOs) improve learning in variational inference, showing they can reduce gradient signal-to-noise ratio and harm inference network training. It introduces three new algorithms (PIWAE, MIWAE, CIWAE) that outperform the standard IWAE, with PIWAE potentially enhancing both inference and generative networks.
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.