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Activity Number: 149
Type: Invited
Date/Time: Monday, August 1, 2016 : 10:30 AM to 12:20 PM
Sponsor: International Chinese Statistical Association
Abstract #318020
Title: A General Framework for Bayes Structured Linear Models
Author(s): Harrison Zhou and Chao Gao*
Companies: Yale University and Yale University
Keywords: Oracle inequality ; Stochastic block model ; Graphon ; Aggregation ; Dictionary learning ; Posterior contraction
Abstract:

High dimensional statistics deals with the challenge of extracting structured informa- tion from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods that can deal with very general high dimensional models. In contrast, Bayes methods have been exten- sively studied in various nonparametric settings and rate optimal posterior contraction results have been established. This paper provides a unified approach to both Bayes high dimensional statistics and Bayes nonparametrics in a general framework of structured linear models. With the proposed two-step model selection prior, we prove a general theorem of posterior contraction under an abstract setting. The main theorem can be used to derive new results on optimal posterior contraction under many complex model settings including stochastic block model, graphon estimation and dictionary learning. It can also be used to re-derive optimal posterior contraction for problems such as sparse linear regression and nonparametric aggregation, which improve upon previous Bayes results for these problems. The key of the success lies in the proposed two-step p


Authors who are presenting talks have a * after their name.

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