On the Statistical Optimality of Optimal Decision Trees
While globally optimal empirical risk minimization (ERM) decision trees have become computationally feasible and empirically successful, rigorous theoretical guarantees for their statistical performance remain limited. In this work, we develop a comprehensive statistical theory for ERM trees under random design in both high-dimensional regression and classification. We first establish sharp oracle inequalities that bound the excess risk of the ERM estimator relative to the best possible approximation achievable by any tree with at most $L$ leaves, thereby characterizing the interpretability-accuracy trade-off. We derive these results using a novel uniform concentration framework based on ...
| Authors | Zineng Xu, Subhro Ghosh, Yan Shuo Tan |
|---|---|
| Primary category | stat.ML |
| Published | 5 March 2026 |
| Last updated at source | 16 March 2026 |
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