A0941
Title: Structure learning with global-local prior-penalty dual
Authors: Jyotishka Datta - Virginia Polytechnic Institute and State University (United States) [presenting]
Anindya Bhadra - Purdue University (United States)
Sayantan Banerjee - Indian Institute of Management Indore (India)
Ksheera Sagar - Purdue University (United States)
Abstract: High-dimensional data with complex dependence structure is routinely observed in many areas of science and engineering, and the problem of sparse precision matrix estimation is one such methodological problem fundamental for network estimation. Although both Bayesian and frequentist approaches exist, obtaining good Bayesian and frequentist properties under the same prior-penalty dual is difficult, complicating justification. Recent developments in precision matrix estimation will be briefly reviewed using global-local shrinkage priors, the state-of-the-art Bayesian tool for sparse signal recovery. Possible solutions that lead to a prior-penalty dual will be proposed, offering fully Bayesian uncertainty quantification and computationally efficient point estimates. The posterior convergence rate of the precision matrix estimate is established, matching the oracle rate and the frequentist consistency of the posterior mode. Computationally efficient algorithms for both optimization and sampling are developed respectively for obtaining the penalized likelihood and fully Bayesian estimation problems. It is also illustrated with a protein-protein interaction network estimation in B-cell lymphoma, and future directions are pointed out.
