A0772
Title: Non-axis aligned space partitioning
Authors: Shufei Ge - ShanghaiTech University (China) [presenting]
Abstract: Space partitioning methods, such as decision trees and the Mondrian processes (MP), are often used to model relational data in multi-dimensional space. However, the flexibility of these methods is often limited by the requirement that the cuts be axis aligned. The binary space partitioning (BSP)-tree process was recently introduced as a generalization of the MP for space partitioning with non-axis aligned cuts in the two-dimensional space. While in practice, usually, there are more than two predictors. Motivated by the need for non-axis aligned cuts for multi-dimensional data, the MP was generalized in an arbitrary space. A sequential Monte Carlo algorithm for inference is derived, and random forest versions are provided. The proposed process is self-consistent, allowing oblique cuts and enabling complex inter-dimensional dependence to be captured in multi-dimensional space. In addition, a novel parallel Bayesian nonparametric approach was proposed to partition images with curves, enabling complex object shapes to be acquired.
