A0918
Title: Recent advances in high-dimensional Bayesian graphical models
Authors: Sayantan Banerjee - Indian Institute of Management Indore (India) [presenting]
Abstract: Advances in technology have resulted in massive datasets collected from all aspects of modern life. Very large datasets appear from internet searches, mobile apps, social networking, cloud computing, and wearable devices, as well as from more traditional sources such as bar-code scanning, satellite imaging, air traffic control, banking, finance, and genomics. Due to the complexity of such datasets, flexible models are required, which often involve many parameters that routinely exceed the available sample size. In such a situation, a meaningful inference is possible only if there is a hidden lower-dimensional structure involving far fewer parameters; that is, the system is sparse. The problem of Bayesian estimation of a high-dimensional precision (inverse covariance) matrix corresponding to a Gaussian graphical model under continuous shrinkage priors is considered. Some recent theoretical and computational advances in this field are discussed. Computationally efficient Markov chain Monte Carlo methods and expectation conditional maximization algorithms are provided, respectively, for fully Bayesian and penalized likelihood problems. They also provide theoretical guarantees of the related methods, including establishing posterior convergence. The approach is also validated through extensive simulation studies and via applications in bioinformatics, psychology, finance, and genomics.
