Hinge Regression Trees and HRT-Boost: Newton-Optimized Oblique Learning for Compact Tabular Models
Learning high-quality oblique decision trees remains a significant challenge due to the discrete and non-convex nature of split optimization. We present the Hinge Regression Tree (HRT) framework, which reframes each oblique split as a nonlinear least-squares problem over two linear predictors whose max/min envelope induces ReLU-like representation capacity. We show that the resulting node-level optimization can be interpreted as a damped Newton method, and we establish the monotonic decrease of the node objective for its backtracking line-search variant. We establish, theoretically, that HRT is a universal approximator with an explicit $O(δ^2)$ approximation rate. Building upon this base ...
| Authors | Hongyi Li, Jun Xu, Hong Yan |
|---|---|
| Primary category | cs.LG |
| Published | 22 May 2026 |
| Last updated at source | 22 May 2026 |
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