Year: 2015
Type: article
Abstract: The promise of Bayesian methods for big data sets has not fully been realized due to the lack of scalable computational algo-rithms. For massive data, it is necessary to store and process subsets on different ma-chines in a distributed manner. We propose a simple, general, and highly efficient ap-proach, 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 Wasser-stein barycenter via a highly efficient lin-ear program. The resulting estimate for the Wasserstein posterior (WASP) has an atomic form, facilitating straightforward estimation of posterior summaries of functionals of in-terest. 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. Exam-ples are provided in complex settings includ-ing Gaussian process regression and nonpara-metric Bayes mixture models. 1
Institutions: Duke University, École Polytechnique Fédérale de Lausanne
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: Large-Scale Sparse Bayesian Modeling, Inference, and Design, Statistical and Applied Mathematical Sciences Institute, Geometric and combinatorial foundations for emerging information and inference systems, Theory and methods for compressive sensing with graphical models, Scalable and Accurate Quantum Tomography, G8972124964, G993971353
OpenAlex ID: W2102028181