Random Tessellation Forests

Shufei Ge; Shijia Wang; Yee Whye Teh; Liangliang Wang; Lloyd T. Elliott

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arXiv · 1906.05440

Random Tessellation Forests

Shufei Ge·Shijia Wang·Yee Whye Teh·Liangliang Wang·Lloyd T. Elliott

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Abstract

Space partitioning methods such as random forests and the Mondrian process are powerful machine learning methods for multi-dimensional and relational data, and are based on recursively cutting a domain. The flexibility of these methods is often limited by the requirement that the cuts be axis aligned. The Ostomachion process and the self-consistent binary space partitioning-tree process were recently introduced as generalizations of the Mondrian process for space partitioning with non-axis aligned cuts in the two dimensional plane. Motivated by the need for a multi-dimensional partitioning tree with non-axis aligned cuts, we propose the Random Tessellation Process (RTP), a framework that includes the Mondrian process and the binary space partitioning-tree process as special cases. We derive a sequential Monte Carlo algorithm for inference, and provide random forest methods. Our process is self-consistent and can relax axis-aligned constraints, allowing complex inter-dimensional dependence to be captured. We present a simulation study, and analyse gene expression data of brain tissue, showing improved accuracies over other methods.

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BibTeX RIS

Shufei Ge, Shijia Wang, Yee Whye Teh, Liangliang Wang, Lloyd T. Elliott. 2019-06-13. Random Tessellation Forests. https://arxiv.org/abs/1906.05440

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