Theory and generation of conditional, scalable sub-Gaussian random fields

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 betwee...

Gaussian Markov Random Fields: Theory and Applications

Deep, Dense, and Low-Rank Gaussian Conditional Random Fields

In this work we introduce a fully-connected graph structure in the Deep Gaussian Conditional Random Field (GCRF) model. For this we express the pairwise interactions between pixels as the inner-products of low-dimensional embeddings, delivered by a new subnetwork of a deep architecture. We efficiently minimize the resulting energy by solving the resulting low-rank linear system with conjugate g...

Markov Random Fields and Conditional Random Fields

Markov chains provided us with a way to model 1D objects such as contours probabilistically, in a way that led to nice, tractable computations. We now consider 2D Markov models. These are more powerful, but not as easy to compute with. In addition we will consider two additional issues. First, we will consider adding observations to our models. These observations are conditioned on the value of...

Sparse Gaussian Conditional Random Fields: Algorithms, Theory, and Application to Energy Forecasting

This paper considers the sparse Gaussian conditional random field, a discriminative extension of sparse inverse covariance estimation, where we use convex methods to learn a high-dimensional conditional distribution of outputs given inputs. The model has been proposed by multiple researchers within the past year, yet previous papers have been substantially limited in their analysis of the metho...