B0586
Title: Bayesian vector autoregression using the tree rank prior
Authors: Leo Duan - University of Florida (United States) [presenting]
Abstract: Vector autoregression is very popular for analyzing the multivariate time series. Besides good predictive performance, it enjoys nice interpretation in the Granger-causality graph --- the past values of some variables are helpful for predicting the others. In the high dimensional setting with $p$ variables, one often relies on the matrix-norm/matrix-rank based regularization to induce sparsity; however, this tends to create too many disconnected graph components that are difficult to interpret. To solve this problem, we propose a new type of low-rankness based on the graph topology --- we define the ``tree rank'' as the number of spanning trees needed to cover the graph. Each spanning tree is a minimalist subgraph with $(p-1)$ edges but connects $p$ nodes. As the result, having the regression coefficients on a few spanning trees leads to both high sparsity and high connectivity. To allow efficient computation and uncertainty quantification on the estimates, we develop a novel graph-based continuous shrinkage prior, that exploits a continuous relaxation for the spanning trees. This prior, which we call ``Tree Rank Prior'', avoids the costly combinatorial search in the graph estimation and enjoys the gradient-based Hamiltonian Monte Carlo algorithm for its posterior estimation. The model is applied to find the Granger causality graph in the functional magnetic resonance imaging data.
