Sharded Bayesian Additive Regression Trees
Machine Learning
2023-06-02 v1 Machine Learning
Statistics Theory
Methodology
Statistics Theory
Abstract
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.
Cite
@article{arxiv.2306.00361,
title = {Sharded Bayesian Additive Regression Trees},
author = {Hengrui Luo and Matthew T. Pratola},
journal= {arXiv preprint arXiv:2306.00361},
year = {2023}
}
Comments
46 pages, 10 figures (Appendix included)