# Kernel of Partition Paths: A Unified Representation for Tree Ensembles

arXiv: https://arxiv.org/abs/2606.18853 · HTML: https://mlsanity.com/paper/2606.18853/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 37 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Builds on (most cited first, 20 of 20)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [A Random Forest Guided Tour](https://mlsanity.com/paper/1511.05741/) (2015)
- [Robustness Verification of Tree-based Models](https://mlsanity.com/paper/1906.03849/) (2019)
- [Large Scale Prediction with Decision Trees](https://mlsanity.com/paper/2104.13881/) (2021)
- [Provably Robust Boosted Decision Stumps and Trees against Adversarial Attacks](https://mlsanity.com/paper/1906.03526/) (2019)
- [Geometry- and Accuracy-Preserving Random Forest Proximities](https://mlsanity.com/paper/2201.12682/) (2022)
- [Hierarchical Shrinkage: improving the accuracy and interpretability of tree-based methods](https://mlsanity.com/paper/2202.00858/) (2022)
- [The Random Forest Kernel and other kernels for big data from random partitions](https://mlsanity.com/paper/1402.4293/) (2014)
- [Minimax optimal rates for Mondrian trees and forests](https://mlsanity.com/paper/1803.05784/) (2018)
- [Fr'echet random forests for metric space valued regression with non euclidean predictors](https://mlsanity.com/paper/1906.01741/) (2019)
- [AutoEncoder by Forest](https://mlsanity.com/paper/1709.09018/) (2017)
- [From global to local MDI variable importances for random forests and when they are Shapley values](https://mlsanity.com/paper/2111.02218/) (2021)
- [Learning Interpretable Characteristic Kernels via Decision Forests](https://mlsanity.com/paper/1812.00029/) (2018)
- [Autoencoding Random Forests](https://mlsanity.com/paper/2505.21441/) (2025)
- [Integrating Random Forests and Generalized Linear Models for Improved Accuracy and Interpretability](https://mlsanity.com/paper/2307.01932/) (2023)
- [MMD-based Variable Importance for Distributional Random Forest](https://mlsanity.com/paper/2310.12115/) (2023)
- [A survey and taxonomy of methods interpreting random forest models](https://mlsanity.com/paper/2407.12759/) (2024)
- [A Powerful Random Forest Featuring Linear Extensions (RaFFLE)](https://mlsanity.com/paper/2502.10185/) (2025)

## Abstract (arXiv)

A recent line of work has reframed individual decision trees as linear models on engineered features associated with their splits, opening routes for oracle inequalities and feature-importance reinterpretation, but leaving open the question of what unified geometric object a forest induces when one indexes its feature map by nodes rather than by splits. The present paper studies that object. KPP indexes the feature map by the nodes of the forest, weighted by a path metric that turns each coordinate into a component of a squared-Euclidean path-isometric embedding. KPP unifies four pillars under a single node-indexed representation whose Gram is non-diagonal and carries a metric: prediction, exact additive attribution, deterministic Lipschitz robust radius in the KPP metric, and uniform Rademacher risk bounds for regression and classification under fixed, honest, or cross-fit conditioning. All probabilistic guarantees are conditional on the representation and are stated under three explicit conditioning regimes; the robust-radius guarantee is deterministic in the KPP metric rather than in a norm on the raw input. Conjectured fast-rate refinements for both regression and classification are stated as open problems and are not claimed as theorems.