Efficient Prediction for Tree Markov Random Fields in a Streaming Model

We consider streaming prediction model for tree Markov Random fields. Given the random field, at any point in time we may perform one of three actions: i) predict a label at a vertex on the tree ii) update by associating a label with a vertex or iii) delete the label at a vertex. Using the standard methodology of belief propagation each such action requires time linear in the size of the tree. We give a method based on an optimal decomposition tree that even in the worst case is an exponential speed-up over belief propagation.