Part of Advances in Neural Information Processing Systems 32 (NeurIPS 2019)
Shufei Ge, Shijia Wang, Yee Whye Teh, Liangliang Wang, Lloyd Elliott
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 plane. Motivated by the need for a multi-dimensional partitioning tree with non-axis aligned cuts, we propose the Random Tessellation Process, a framework that includes the Mondrian process as a special case. We derive a sequential Monte Carlo algorithm for inference, and provide random forest methods. Our methods are self-consistent and can relax axis-aligned constraints, allowing complex inter-dimensional dependence to be captured. We present a simulation study and analyze gene expression data of brain tissue, showing improved accuracies over other methods.