A Neural Tangent Kernel Perspective of Infinite Tree Ensembles
This provides foundational insights for machine learning practitioners using tree ensembles, though it is incremental in extending NTK theory to a new model class.
The paper tackles the lack of theoretical understanding of infinite soft tree ensembles by introducing the Tree Neural Tangent Kernel (TNTK), which reveals properties like global convergence and kernel degeneracy with tree deepening.
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.