Scalable Bayesian High-dimensional Local Dependence Learning

In this work, we propose a scalable Bayesian procedure for learning the local dependence structure in high-dimensional model where variables possess natural ordering. The ordering of can be indexed by time, vicinities spatial locations, and so on, with assumption that far apart tend to have weak correlations. Applications such models abound variety fields as finance, genome associations analysis modeling. We adopt flexible framework under which each variable is dependent on its neighbors or predecessors, neighborhood size vary variable. It great interest reveal estimating covariance precision matrix while yielding consistent estimate varying existing literature banded estimation, assumes fixed bandwidth cannot adapted general setup. employ modified Cholesky decomposition design prior through appropriate priors sizes factors. posterior contraction rates factor are derived nearly exactly minimax optimal, our leads estimates all variables. Another appealing feature scalability large numbers due efficient inference without resorting MCMC algorithms. Numerical comparisons carried out competitive methods, applications considered some real datasets.