# LHT: Statistically-Driven Oblique Decision Trees for Interpretable Classification

arXiv: https://arxiv.org/abs/2505.04139 · HTML: https://mlsanity.com/paper/2505.04139/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 7 May 2025.

## Builds on (most cited first, 9 of 9)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [Efficient non-greedy optimization of decision trees](https://mlsanity.com/paper/1511.04056/) (2015)
- [Learning Accurate Decision Trees with Bandit Feedback via Quantized Gradient Descent](https://mlsanity.com/paper/2102.07567/) (2021)
- [GradTree: Learning Axis-Aligned Decision Trees with Gradient Descent](https://mlsanity.com/paper/2305.03515/) (2023)
- [Trained Random Forests Completely Reveal your Dataset](https://mlsanity.com/paper/2402.19232/) (2024)
- [Vanilla Gradient Descent for Oblique Decision Trees](https://mlsanity.com/paper/2408.09135/) (2024)
- [CO2 Forest: Improved Random Forest by Continuous Optimization of Oblique Splits](https://mlsanity.com/paper/1506.06155/) (2015)
- [Convex Polytope Trees](https://mlsanity.com/paper/2010.11266/) (2020)

## Built on by (most cited first, 1 of 1)

- [A Geometrical Approach to Constructing Neural Networks for Perfect Training-set Classification](https://mlsanity.com/paper/2610.17312/) (2026)

## Abstract (arXiv)

We introduce the Learning Hyperplane Tree (LHT), a novel oblique decision tree model designed for expressive and interpretable classification. LHT fundamentally distinguishes itself through a non-iterative, statistically-driven approach to constructing splitting hyperplanes. Unlike methods that rely on iterative optimization or heuristics, LHT directly computes the hyperplane parameters, which are derived from feature weights based on the differences in feature expectations between classes within each node. This deterministic mechanism enables a direct and well-defined hyperplane construction process. Predictions leverage a unique piecewise linear membership function within leaf nodes, obtained via local least-squares fitting. We formally analyze the convergence of the LHT splitting process, ensuring that each split yields meaningful, non-empty partitions. Furthermore, we establish that the time complexity for building an LHT up to depth d is O(mnd), demonstrating the practical feasibility of constructing trees with powerful oblique splits using this methodology. The explicit feature weighting at each split provides inherent interpretability. Experimental results on benchmark datasets demonstrate LHT's competitive accuracy, positioning it as a practical, theoretically grounded, and interpretable alternative in the landscape of tree-based models. The implementation of the proposed method is available at https://github.com/Hongyi-Li-sz/LHTmodel.