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About this paper
Akash Kumar Dhaka, Alejandro Catalina, Manushi Welandawe, Michael Riis Andersen, Jonathan Huggins, Aki Vehtari
Researchers at Aalto University, Boston University, and Technical University of Denmark introduce a framework to assess the reliability of black-box variational inference (BBVI) by analyzing the pre-asymptotic tail behavior of density ratios. Their work demonstrates that mode-seeking divergences, particularly exclusive KL, provide superior optimization stability and approximation accuracy in high-dimensional posteriors compared to mass-covering divergences.
Key insights
- Mode-seeking divergences (e.g., exclusive KL) exhibit substantially lower bias and variance in estimates and gradients, offering superior optimization stability in higher dimensions compared to mass-covering divergences.
- The Pareto k diagnostic reliably indicates the pre-asymptotic stability of variational objectives; values above 0.7 signal unreliability due to fundamental mismatches between the typical sets of the target and approximate distributions.
- Flexible variational families like normalizing flows are most effective when paired with stable divergences (like exclusive KL) and significantly benefit from post-hoc importance sampling (e.g., PSIS) for refining high-dimensional posterior estimates.
Summary by alphaXiv.
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