Extending the Modelling Capacity of Gaussian Conditional Random Fields while Learning Faster

Abstract

Gaussian Conditional Random Fields (GCRF) are a type of structured regression model that incorporates multiple predictors and multiple graphs. This is achieved by defining quadratic term feature functions in Gaussian canonical form which makes the conditional log-likelihood function convex and hence allows finding the optimal parameters by learning from data. In this work, the parameter space for the GCRF model is extended to facilitate joint modelling of positive and negative influences. This is achieved by restricting the model to a single graph and formulating linear bounds on convexity with respect to the models parameters. In addition, our formulation for the model using one network allows calculating gradients much faster than alternative implementations. Lastly, we extend the model one step farther and incorporate a bias term into our link weight. This bias is solved as part of the convex optimization. Benefits of the proposed model in terms of improved accuracy and speed are characterized on several synthetic graphs with 2 million links as well as on a hospital admissions prediction task represented as a human disease-symptom similarity network corresponding to more than 35 million hospitalization records in California over 9 years.