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.Comment: 11 pages, 4 figure
