Structural algorithms incorporate the interdependence of outputs into the prediction, the loss, or both. Frank-Wolfe optimizations of pairwise losses and Gaussian conditional random fields for multivariate output regression are two such structural algorithms. Pairwise losses are standard 0-1 classification surrogate losses applied to pairs of features and outputs, resulting in improved ranking performance (area under the ROC curve, average precision, and F-1 score) at the cost of increased learning complexity. In this dissertation, it is proven that the balanced loss 0-1 SVM and the pairwise SVM have the same dual loss and the pairwise dual coefficient domain is a subdomain of the balanced loss 0-1 SVM with bias dual coefficient domain. This provides a theoretical advancement in the understanding of pairwise loss, which we exploit for the development of a novel ranking algorithm that is fast and memory efficient method with state the art ranking metric performance across eight benchmark data sets. Various practical advancements are also made in multivariate output regression. The learning time for Gaussian conditional random fields is greatly reduced and the parameter domain is expanded to enable repulsion between outputs. Last, a novel multivariate regression is presented that keeps the desirable elements of GCRF and infuses them into a local regression model that improves mean squared error and reduces learning complexity. / Computer and Information Science