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Keywords: regression trees, streaming data, dynamic models
The dynamic Bayesian regression tree is a flexible regression model for sequential data that permits the relationship between the response and explanatory variables to evolve smoothly over time through a latent process. This paper shows that exact sequential inference can be performed via implementation of the intermittent Kalman filter, permitting fast computation. Inference on the tree structure is done through a random forest approach and an exact expression for the posterior weight of each tree in the forest is derived. Its main novel contribution is to place this in a streaming data setting, where there is information about the rate at which data are arriving, and the model complexity is tuned to a level for which the computation can be done at a rate that permits the streaming analysis.