A Neural Tangent Kernel Perspective of Infinite Tree Ensembles

TL;DR

This paper introduces the Tree Neural Tangent Kernel (TNTK) to analyze infinite soft tree ensembles, providing theoretical insights into their convergence, structure, and degeneracy.

Contribution

It develops a novel TNTK framework for understanding infinite soft tree ensembles, bridging a gap in theoretical analysis.

Findings

Global convergence of training with TNTK

Equivalence of oblivious tree structures

Degeneracy of TNTK with increasing tree depth

Abstract

In practical situations, the tree ensemble is one of the most popular models along with neural networks. A soft tree is a variant of a decision tree. Instead of using a greedy method for searching splitting rules, the soft tree is trained using a gradient method in which the entire splitting operation is formulated in a differentiable form. Although ensembles of such soft trees have been used increasingly in recent years, little theoretical work has been done to understand their behavior. By considering an ensemble of infinite soft trees, this paper introduces and studies the Tree Neural Tangent Kernel (TNTK), which provides new insights into the behavior of the infinite ensemble of soft trees. Using the TNTK, we theoretically identify several non-trivial properties, such as global convergence of the training, the equivalence of the oblivious tree structure, and the degeneracy of the TNTK induced by the deepening of the trees.