Challenges for BBVI with Normalizing Flows
Current black-box variational inference (BBVI) methods require the user to make numerous design choices---such as the selection of variational objective and approximating family---yet there is little principled guidance on how to do so. We develop a conceptual framework and set of experimental tools to understand the effects of these choices, which we leverage to propose best practices for maximizing posterior approximation accuracy. Our approach is based on studying the pre-asymptotic tail behavior of the density ratios between the joint distribution and the variational approximation, then exploiting insights and tools from the importance sampling literature. We focus on normalizing flow models and give recommendations on how to be used(and diagnostics) in BBVI, though we are not limited to them.
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