Variational Inference and Model Selection with Generalized Evidence Bounds

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Liqun Chen, Chenyang Tao, Ruiyi Zhang, Ricardo Henao, Lawrence Carin Duke ;
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:893-902, 2018.

Abstract

Recent advances on the scalability and flexibility of variational inference have made it successful at unravelling hidden patterns in complex data. In this work we propose a new variational bound formulation, yielding an estimator that extends beyond the conventional variational bound. It naturally subsumes the importance-weighted and Renyi bounds as special cases, and it is provably sharper than these counterparts. We also present an improved estimator for variational learning, and advocate a novel high signal-to-variance ratio update rule for the variational parameters. We discuss model-selection issues associated with existing evidence-lower-bound-based variational inference procedures, and show how to leverage the flexibility of our new formulation to address them. Empirical evidence is provided to validate our claims.

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