# Positive-Unlabeled Learning using Random Forests via Recursive Greedy Risk Minimization

arXiv: https://arxiv.org/abs/2210.08461 · HTML: https://mlsanity.com/paper/2210.08461/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 40 references that are in the map.
- First posted on arXiv 16 Oct 2022.

## Builds on (most cited first, 8 of 8)

- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (2018)
- [Approximating Continuous Functions by ReLU Nets of Minimal Width](https://mlsanity.com/paper/1710.11278/) (2017)
- [Mixture Proportion Estimation via Kernel Embedding of Distributions](https://mlsanity.com/paper/1603.02501/) (2016)
- [Self-PU: Self Boosted and Calibrated Positive-Unlabeled Training](https://mlsanity.com/paper/2006.11280/) (2020)
- [Class-prior Estimation for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1611.01586/) (2016)
- [Instance-Dependent PU Learning by Bayesian Optimal Relabeling](https://mlsanity.com/paper/1808.02180/) (2018)

## Built on by (most cited first, 8 of 8)

- [Beyond Myopia: Learning from Positive and Unlabeled Data through Holistic Predictive Trends](https://mlsanity.com/paper/2310.04078/) (2023)
- [Class Prior-Free Positive-Unlabeled Learning with Taylor Variational Loss for Hyperspectral Remote Sensing Imagery](https://mlsanity.com/paper/2308.15081/) (2023)
- [Community-Based Hierarchical Positive-Unlabeled (PU) Model Fusion for Chronic Disease Prediction](https://mlsanity.com/paper/2309.03386/) (2023)
- [Robust Loss Functions for Training Decision Trees with Noisy Labels](https://mlsanity.com/paper/2312.12937/) (2023)
- [Noisy-Pair Robust Representation Alignment for Positive-Unlabeled Learning](https://mlsanity.com/paper/2510.01278/) (2025)
- [Regression with Sensor Data Containing Incomplete Observations](https://mlsanity.com/paper/2304.13415/) (2023)
- [HOpenCls: Training Hyperspectral Image Open-Set Classifiers in Their Living Environments](https://mlsanity.com/paper/2502.15163/) (2025)
- [An Effective Flow-based Method for Positive-Unlabeled Learning: 2-HNC](https://mlsanity.com/paper/2505.08212/) (2025)

## Abstract (arXiv)

The need to learn from positive and unlabeled data, or PU learning, arises in many applications and has attracted increasing interest. While random forests are known to perform well on many tasks with positive and negative data, recent PU algorithms are generally based on deep neural networks, and the potential of tree-based PU learning is under-explored. In this paper, we propose new random forest algorithms for PU-learning. Key to our approach is a new interpretation of decision tree algorithms for positive and negative data as recursive greedy risk minimization algorithms. We extend this perspective to the PU setting to develop new decision tree learning algorithms that directly minimizes PU-data based estimators for the expected risk. This allows us to develop an efficient PU random forest algorithm, PU extra trees. Our approach features three desirable properties: it is robust to the choice of the loss function in the sense that various loss functions lead to the same decision trees; it requires little hyperparameter tuning as compared to neural network based PU learning; it supports a feature importance that directly measures a feature's contribution to risk minimization. Our algorithms demonstrate strong performance on several datasets. Our code is available at urlhttps://github.com/puetpaper/PUExtraTrees.