The Binary Space Partitioning-Tree Process
This work addresses a domain-specific problem in space partition modelling for researchers, offering an incremental generalization of the Mondrian process.
The authors tackled the limited flexibility of the Mondrian process by proposing a self-consistent Binary Space Partitioning-Tree process that allows oblique cuts, resulting in clear inferential improvements over the standard Mondrian process and other methods on synthetic data partitioning and relational modelling.
The Mondrian process represents an elegant and powerful approach for space partition modelling. However, as it restricts the partitions to be axis-aligned, its modelling flexibility is limited. In this work, we propose a self-consistent Binary Space Partitioning (BSP)-Tree process to generalize the Mondrian process. The BSP-Tree process is an almost surely right continuous Markov jump process that allows uniformly distributed oblique cuts in a two-dimensional convex polygon. The BSP-Tree process can also be extended using a non-uniform probability measure to generate direction differentiated cuts. The process is also self-consistent, maintaining distributional invariance under a restricted subdomain. We use Conditional-Sequential Monte Carlo for inference using the tree structure as the high-dimensional variable. The BSP-Tree process's performance on synthetic data partitioning and relational modelling demonstrates clear inferential improvements over the standard Mondrian process and other related methods.