# Random Tessellation Forests

## TL;DR

The paper introduces the Random Tessellation Process, a flexible space partitioning framework that generalizes existing methods by allowing non-axis aligned cuts, improving modeling of complex inter-dimensional dependencies.

## Contribution

It proposes the RTP framework that unifies and extends previous space partitioning methods, with a new inference algorithm and applications to gene expression data.

## Key findings

- Improved accuracy in gene expression data analysis.
- Flexible modeling of multi-dimensional dependencies.
- Unified framework encompassing existing partitioning methods.

## 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.