The Discrete Gaussian Expectation Maximization (Gradient) Algorithm for Differential Privacy.

Area of Science:

• Data privacy
• Machine learning
• High-dimensional data analysis

Background:

• Protecting sensitive data in high-dimensional datasets is crucial.
• Existing methods may not offer sufficient privacy guarantees or efficiency.
• The Expectation-Maximization (EM) algorithm is widely used but can be vulnerable.

Purpose of the Study:

• To develop a privacy-preserving gradient EM algorithm for high-dimensional data.
• To enhance data processing efficiency through specific data manipulation techniques.
• To improve differential privacy guarantees using the discrete Gaussian mechanism.

Main Methods:

• A modified gradient EM algorithm incorporating a discrete Gaussian mechanism for noise addition.
• Data preprocessing steps including scaling, truncation, noise multiplication, and smoothing.
• Comparative analysis against standard gradient EM and clipped algorithms using a Gaussian Mixture Model (GMM).

Main Results:

• The proposed algorithm (DG-EM) effectively protects the privacy of high-dimensional sensitive data.
• Discrete Gaussian noise offers improved privacy compared to continuous Gaussian noise due to smaller variance.
• The algorithm demonstrated robust performance in experimental evaluations.

Conclusions:

• The DG-EM algorithm provides an effective solution for privacy-preserving analysis of high-dimensional data.
• The discrete Gaussian mechanism enhances differential privacy guarantees.
• This approach facilitates secure and efficient machine learning on sensitive datasets.