Abstract: A new tractable model solves labeling problems using regression tree fields, which represent non-parametric Gaussian conditional random fields. Regression tree fields are parameterized by non-parametric regression trees, allowing universal specification of interactions between image observations and variables. The new model uses regression trees corresponding to various factors to map dataset content (e.g., image content) to a set of parameters used to define the potential functions in the model. Some factors define relationships among multiple variable nodes. Further, the training of regression trees is scalable, both in the training set size and in the fact that the training can be parallelized. In one implementation, maximum pseudolikelihood learning provides for joint training of various aspects of the model, including feature test selection and ordering (i.e., the structure of the regression trees), parameters of each factor in the graph, and the scope of the interacting variable nodes used in the graph.