Low rank continuous-space graphical models

Constructing tractable dependent probability distributions over structured continuous random vectors is a central problem in statistics and machine learning. It has proven difficult to find general constructions for models in which ecient exact inference is possible, outside of the classical cases of models with restricted graph structure (chain, tree, etc.) and linear-Gaussian or discrete potentials. In this work we identify a graphical model class in which exact inference can be performed efficiently, owing to a certain “low-rank” structure in the potentials. While we focus on the case of tree graphical models, the lowrank treatment can also be applied for ecient exact inference in certain sparsely-loopy models. We explore this new class of models by applying the resulting inference methods to neural spike rate estimation and motioncapture joint-angle smoothing tasks.