Decision trees and the Mondrian processes (MPs) are powerful space-partitioning methodsfor relational data in multi-dimensional space. These methods are based onrecursively cutting a domain, the flexibility of these methods is often limitedby the requirement that the cuts be axis aligned. The binary space partitioning(BSP)-tree process was recently introduced as a generalization of the MP forspace partitioning with non-axis aligned cuts in the two-dimensional space.Motivated by these processes, we propose the Random Tessellation Process (RTP),a framework that includes the MP and the BSP-tree process as special cases. Wederive a sequential Monte Carlo algorithm for inference and provide randomforest versions. The RTP is self-consistent and can relax axis-alignedconstraints, allowing complex inter-dimensional dependence to be captured inmulti-dimensional space. Moreover, we propose a novel parallel Bayesiannonparametric approach to split a two-dimensional domain with the Bézier curvesin the framework of space partitioning methods, enabling complex data-shapes tobe acquired.
Shufei Ge is anassistant professor at the Institute of Mathematical Sciences, ShanghaiTechUniversity, where she has been a faculty member since Sep. of 2020. Beforethat, she received her Ph.D. in statistics at Simon Fraser University, Canada.Her research interest involves Bayesian statistics, statistical machinelearning methods and computational biology. She has published papers instatistical journals and machine learning conferences, including the Advancesin Neural Information Processing Systems, Biometrics, Bioinformatics, andJournal of Computational and Graphical Statistics.