A0326
Title: Geometric shapes of the tree-induced partition
Authors: Hengrui Luo - Rice University (United States) [presenting]
Abstract: Decision trees are a crucial class of regression methods in modern statistics and machine learning. Traditionally, these methods create partitions in the form of nested rectangles. However, real-world applications often demand more flexible and irregular partition shapes. The computational complexity and scalability of decision trees when dealing with such irregular geometric partitions are explored. It demonstrates how decision trees effectively create multidimensional boundaries to divide the input space, highlighting the increased search difficulty and computational challenges that arise. To address these complexities, an innovative tensor-on-tensor tree regression approach is introduced, specifically designed to handle multidimensional geometric partitioning. Finally, the fundamental geometric principles underlying tree-induced partitions are reflected on, and future research directions at the intersection of geometry and tree-based models are considered.
