Neural Gaussian Conditional Random Fields

We propose a Conditional Random Field (CRF) model for structured regression. By constraining the feature functions as quadratic functions of outputs, the model can be conveniently represented in a Gaussian canonical form. We improved the representational power of the resulting Gaussian CRF (GCRF) model by (1) introducing an adaptive feature function that can learn nonlinear relationships between inputs and outputs and (2) allowing the weights of feature functions to be dependent on inputs. Since both the adaptive feature functions and weights can be constructed using feedforward neural networks, we call the resulting model Neural GCRF. The appeal of Neural GCRF is in conceptual simplicity and computational efficiency of learning and inference through use of sparse matrix computations. Experimental evaluation on the remote sensing problem of aerosol estimation from satellite measurements and on the problem of document retrieval showed that Neural GCRF is more accurate than the benchmark predictors.