Sharded Bayesian Additive Regression Trees
Hengrui Luo Matthew T. Pratola
In this paper we develop the randomized Sharded Bayesian Additive Regression
Trees (SBT) model. We introduce a randomization auxiliary variable and a
sharding tree to decide partitioning of data, and fit each partition component
to a sub-model using Bayesian Additive Regression Tree (BART). By observing
that the optimal design of a sharding tree can determine optimal sharding for
sub-models on a product space, we introduce an intersection tree structure to
completely specify both the sharding and modeling using only tree structures.
In addition to experiments, we also derive the theoretical optimal weights for
minimizing posterior contractions and prove the worst-case complexity of SBT.