# Preserving Differential Privacy in Convolutional Deep Belief Networks

arXiv: https://arxiv.org/abs/1706.08839 · HTML: https://mlsanity.com/paper/1706.08839/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2017.

## Built on by (most cited first, 9 of 9)

- [How to DP-fy ML: A Practical Guide to Machine Learning with Differential Privacy](https://mlsanity.com/paper/2303.00654/) (2023)
- [Recent Advances of Differential Privacy in Centralized Deep Learning: A Systematic Survey](https://mlsanity.com/paper/2309.16398/) (2023)
- [Privacy-preserving machine learning with tensor networks](https://mlsanity.com/paper/2202.12319/) (2022)
- [A Differentially Private Framework for Deep Learning with Convexified Loss Functions](https://mlsanity.com/paper/2204.01049/) (2022)
- [FairDP: Certified Fairness with Differential Privacy](https://mlsanity.com/paper/2305.16474/) (2023)
- [Lifelong DP: Consistently Bounded Differential Privacy in Lifelong Machine Learning](https://mlsanity.com/paper/2207.12831/) (2022)
- [Training with Differential Privacy: A Gradient-Preserving Noise Reduction Approach with Provable Security](https://mlsanity.com/paper/2409.11663/) (2024)
- [Deep Learning under Fractional-Order Differential Privacy](https://mlsanity.com/paper/2605.09890/) (2026)
- [An exponential mechanism based on quadratic approximations for fine-tuning machine learning models with privacy guarantees](https://mlsanity.com/paper/2605.20521/) (2026)

## Abstract (arXiv)

The remarkable development of deep learning in medicine and healthcare domain presents obvious privacy issues, when deep neural networks are built on users' personal and highly sensitive data, e.g., clinical records, user profiles, biomedical images, etc. However, only a few scientific studies on preserving privacy in deep learning have been conducted. In this paper, we focus on developing a private convolutional deep belief network (pCDBN), which essentially is a convolutional deep belief network (CDBN) under differential privacy. Our main idea of enforcing epsilon-differential privacy is to leverage the functional mechanism to perturb the energy-based objective functions of traditional CDBNs, rather than their results. One key contribution of this work is that we propose the use of Chebyshev expansion to derive the approximate polynomial representation of objective functions. Our theoretical analysis shows that we can further derive the sensitivity and error bounds of the approximate polynomial representation. As a result, preserving differential privacy in CDBNs is feasible. We applied our model in a health social network, i.e., YesiWell data, and in a handwriting digit dataset, i.e., MNIST data, for human behavior prediction, human behavior classification, and handwriting digit recognition tasks. Theoretical analysis and rigorous experimental evaluations show that the pCDBN is highly effective. It significantly outperforms existing solutions.