Variational inference via χ upper bound minimization

Adji B. Dieng, Dustin Tran, Rajesh Ranganath, John Paisley, David M. Blei

Research output: Contribution to journalConference articlepeer-review

72 Scopus citations


Variational inference (VI) is widely used as an efficient alternative to Markov chain Monte Carlo. It posits a family of approximating distributions q and finds the closest member to the exact posterior p. Closeness is usually measured via a divergence D(q\ \p) from q to p. While successful, this approach also has problems. Notably, it typically leads to underestimation of the posterior variance. In this paper we propose CHIVI, a black-box variational inference algorithm that minimizes Dx(p\\q), the χ-divergence fromp to q. CHIVI minimizes an upper bound of the model evidence, which we term the χ upper bound (CUBO). Minimizing the CUBO leads to improved posterior uncertainty, and it can also be used with the classical VI lower bound (ELBO) to provide a sandwich estimate of the model evidence. We study CHIVI on three models: probit regression, Gaussian process classification, and a Cox process model of basketball plays. When compared to expectation propagation and classical VI, CHIVI produces better error rates and more accurate estimates of posterior variance.

Original languageEnglish (US)
Pages (from-to)2733-2742
Number of pages10
JournalAdvances in Neural Information Processing Systems
StatePublished - 2017
Externally publishedYes
Event31st Annual Conference on Neural Information Processing Systems, NIPS 2017 - Long Beach, United States
Duration: Dec 4 2017Dec 9 2017

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


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