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WASP: Scalable Bayes via barycenters of subset posteriors

Publication ,  Conference
Srivastava, S; Cevher, V; Tran-Dinh, Q; Dunson, DB
Published in: Journal of Machine Learning Research
January 1, 2015

The promise of Bayesian methods for big data sets has not fully been realized due to the lack of scalable computational algorithms. For massive data, it is necessary to store and process subsets on different machines in a distributed manner. We propose a simple, general, and highly efficient approach, which first runs a posterior sampling algorithm in parallel on different machines for subsets of a large data set. To combine these subset posteriors, we calculate the Wasserstein barycenter via a highly efficient linear program. The resulting estimate for the Wasserstein posterior (WASP) has an atomic form, facilitating straightforward estimation of posterior summaries of functionals of interest. The WASP approach allows posterior sampling algorithms for smaller data sets to be trivially scaled to huge data. We provide theoretical justification in terms of posterior consistency and algorithm efficiency. Examples are provided in complex settings including Gaussian process regression and nonparametric Bayes mixture models.

Duke Scholars

Published In

Journal of Machine Learning Research

EISSN

1533-7928

ISSN

1532-4435

Publication Date

January 1, 2015

Volume

38

Start / End Page

912 / 920

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4905 Statistics
  • 4611 Machine learning
  • 17 Psychology and Cognitive Sciences
  • 08 Information and Computing Sciences
 

Citation

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Srivastava, S., Cevher, V., Tran-Dinh, Q., & Dunson, D. B. (2015). WASP: Scalable Bayes via barycenters of subset posteriors. In Journal of Machine Learning Research (Vol. 38, pp. 912–920).
Srivastava, S., V. Cevher, Q. Tran-Dinh, and D. B. Dunson. “WASP: Scalable Bayes via barycenters of subset posteriors.” In Journal of Machine Learning Research, 38:912–20, 2015.
Srivastava S, Cevher V, Tran-Dinh Q, Dunson DB. WASP: Scalable Bayes via barycenters of subset posteriors. In: Journal of Machine Learning Research. 2015. p. 912–20.
Srivastava, S., et al. “WASP: Scalable Bayes via barycenters of subset posteriors.” Journal of Machine Learning Research, vol. 38, 2015, pp. 912–20.
Srivastava S, Cevher V, Tran-Dinh Q, Dunson DB. WASP: Scalable Bayes via barycenters of subset posteriors. Journal of Machine Learning Research. 2015. p. 912–920.

Published In

Journal of Machine Learning Research

EISSN

1533-7928

ISSN

1532-4435

Publication Date

January 1, 2015

Volume

38

Start / End Page

912 / 920

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4905 Statistics
  • 4611 Machine learning
  • 17 Psychology and Cognitive Sciences
  • 08 Information and Computing Sciences