# Privacy-Preserving Training of Tree Ensembles over Continuous Data

arXiv: https://arxiv.org/abs/2106.02769 · HTML: https://mlsanity.com/paper/2106.02769/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 55 references that are in the map.
- First posted on arXiv 5 Jun 2021.

## Builds on (most cited first, 6 of 6)

- [Protecting Privacy of Users in Brain-Computer Interface Applications](https://mlsanity.com/paper/1907.01586/) (2019)
- [High Performance Logistic Regression for Privacy-Preserving Genome Analysis](https://mlsanity.com/paper/2002.05377/) (2020)
- [Secure multiparty computations in floating-point arithmetic](https://mlsanity.com/paper/2001.03192/) (2020)
- [Privacy-Preserving Classification of Personal Text Messages with Secure Multi-Party Computation: An Application to Hate-Speech Detection](https://mlsanity.com/paper/1906.02325/) (2019)
- [Weakening the Isolation Assumption of Tamper-proof Hardware Tokens](https://mlsanity.com/paper/1502.03487/) (2015)
- [A Framework for Efficient Adaptively Secure Composable Oblivious Transfer in the ROM](https://mlsanity.com/paper/1710.08256/) (2017)

## Built on by (most cited first, 5 of 5)

- [Secure Multiparty Computation for Synthetic Data Generation from Distributed Data](https://mlsanity.com/paper/2210.07332/) (2022)
- [Eliminating Label Leakage in Tree-Based Vertical Federated Learning](https://mlsanity.com/paper/2307.10318/) (2023)
- [Ensembling Neural Networks for Improved Prediction and Privacy in Early Diagnosis of Sepsis](https://mlsanity.com/paper/2209.00439/) (2022)
- [Training Differentially Private Models with Secure Multiparty Computation](https://mlsanity.com/paper/2202.02625/) (2022)
- [Ents: An Efficient Three-party Training Framework for Decision Trees by Communication Optimization](https://mlsanity.com/paper/2406.07948/) (2024)

## Abstract (arXiv)

Most existing Secure Multi-Party Computation (MPC) protocols for privacy-preserving training of decision trees over distributed data assume that the features are categorical. In real-life applications, features are often numerical. The standard ``in the clear'' algorithm to grow decision trees on data with continuous values requires sorting of training examples for each feature in the quest for an optimal cut-point in the range of feature values in each node. Sorting is an expensive operation in MPC, hence finding secure protocols that avoid such an expensive step is a relevant problem in privacy-preserving machine learning. In this paper we propose three more efficient alternatives for secure training of decision tree based models on data with continuous features, namely: (1) secure discretization of the data, followed by secure training of a decision tree over the discretized data; (2) secure discretization of the data, followed by secure training of a random forest over the discretized data; and (3) secure training of extremely randomized trees (``extra-trees'') on the original data. Approaches (2) and (3) both involve randomizing feature choices. In addition, in approach (3) cut-points are chosen randomly as well, thereby alleviating the need to sort or to discretize the data up front. We implemented all proposed solutions in the semi-honest setting with additive secret sharing based MPC. In addition to mathematically proving that all proposed approaches are correct and secure, we experimentally evaluated and compared them in terms of classification accuracy and runtime. We privately train tree ensembles over data sets with 1000s of instances or features in a few minutes, with accuracies that are at par with those obtained in the clear. This makes our solution orders of magnitude more efficient than the existing approaches, which are based on oblivious sorting.