Gaussian conditional random fields extended for directed graphs

For many real-world applications, structured regression is commonly used for predicting output variables that have some internal structure. Gaussian conditional random fields (GCRF) are a widely used type of structured regression model that incorporates the outputs of unstructured predictors and the correlation between objects in order to achieve higher accuracy. However, applications of this model are limited to objects that are symmetrically correlated, while interaction between objects is asymmetric in many cases. In this work we propose a new model, called Directed Gaussian conditional random fields (DirGCRF), which extends GCRF to allow modeling asymmetric relationships (e.g. friendship, influence, love, solidarity, etc.). The DirGCRF models the response variable as a function of both the outputs of unstructured predictors and the asymmetric structure. The effectiveness of the proposed model is characterized on six types of synthetic datasets and four real-world applications where DirGCRF was consistently more accurate than the standard GCRF model and baseline unstructured models.