Graphical model estimation from incomplete data and auxiliary variables

Music City Center 

Probabilistic graphical models are essential for analyzing large multivariate data. However, data missingness can hinder graphical model estimation when a complete sample covariance matrix is unavailable. We propose new methods to estimate a complete graphical model from incomplete data with the help of auxiliary variables that may be informative about the variables' dependence structure. For instance, the dependence between two neurons typically weakens as the distance between them increases. We investigate two approaches: (a) estimating a sparse graphical model based on a sample covariance matrix completed via the previously proposed AuxCov method, which assumes a relationship between correlations and auxiliary variables; and (b) directly estimating a complete precision matrix by applying a penalty that reflects the relationship between partial correlations and auxiliary variables. We assess our methods theoretically, through simulations, and by analyzing large-scale neuroscience data.

conditional dependence

cross validation

graphical lasso

matrix completion

multivariate analysis

sparsity 

IMS