Online Binary Space Partitioning Forests

TL;DR

This paper introduces an online BSP-Forest framework that enhances space partitioning efficiency for large-scale classification and regression tasks, maintaining consistency and demonstrating strong performance on real datasets.

Contribution

It develops an online version of the BSP-Tree Forest, enabling real-time updates and improved scalability for space partitioning in classification and regression.

Findings

Achieves universal consistency for classification and regression.

Demonstrates competitive performance on real-world datasets.

Effectively expands space coverage with new data.

Abstract

The Binary Space Partitioning-Tree~(BSP-Tree) process was recently proposed as an efficient strategy for space partitioning tasks. Because it uses more than one dimension to partition the space, the BSP-Tree Process is more efficient and flexible than conventional axis-aligned cutting strategies. However, due to its batch learning setting, it is not well suited to large-scale classification and regression problems. In this paper, we develop an online BSP-Forest framework to address this limitation. With the arrival of new data, the resulting online algorithm can simultaneously expand the space coverage and refine the partition structure, with guaranteed universal consistency for both classification and regression problems. The effectiveness and competitive performance of the online BSP-Forest is verified via simulations on real-world datasets.