Bayesian Nonparametric Space Partitions: A Survey

Abstract

Bayesian nonparametric space partition (BNSP) models provide a variety of strategies for partitioning a $D$-dimensional space into a set of blocks. In this way, the data points lie in the same block would share certain kinds of homogeneity. BNSP models can be applied to various areas, such as regression/classification trees, random feature construction, relational modeling, etc. In this survey, we investigate the current progress of BNSP research through the following three perspectives: models, which review various strategies for generating the partitions in the space and discuss their theoretical foundation `self-consistency'; applications, which cover the current mainstream usages of BNSP models and their potential future practises; and challenges, which identify the current unsolved problems and valuable future research topics. As there are no comprehensive reviews of BNSP literature before, we hope that this survey can induce further exploration and exploitation on this topic.

References in corpus (7)

• Stochastic blockmodels and community structure in networks
• Mondrian Forests: Efficient Online Random Forests
• Non-parametric Bayesian modeling of complex networks
• Analysis of purely random forests bias
• The Binary Space Partitioning-Tree Process
• Rectangular Bounding Process
• Binary Space Partitioning Forests

Cited by in corpus (2)

• (Decision and regression) tree ensemble based kernels for regression and classification
• A Framework for an Assessment of the Kernel-target Alignment in Tree Ensemble Kernel Learning