UCLA

This thesis introduces an algorithm for estimating Gaussian graphical models from multiple subpopulations sharing some dependence structure. The algorithm uses proximal gradient descent to estimate solutions to a neighborhood regression problem along with L1 and graph Laplacian penalty terms. The graph Laplacian penalty term induces similarity amongst neighborhood regression coefficients belonging to subpopulations known to share much dependence structure. Further, the algorithm can be distributed amongst agents and a server to ensure that agents do not share their datasets with each other. The distributed algorithm is equivalent to the non-distributed algorithm from an input-output perspective. The algorithm is compared with the graphical lasso on multiple synthetic datasets.