A Moment Matching Approach for Generating Synthetic Data.

Area of Science:

• Data Science
• Statistical Modeling
• Computational Statistics

Background:

• Synthetic data generation is crucial for data sharing but existing methods struggle to preserve original statistical properties.
• Current techniques often have limitations in maintaining data integrity and statistical fidelity.
• Need for robust synthetic data methods that ensure privacy and statistical accuracy.

Purpose of the Study:

• To introduce a novel fully synthetic data generation method using mathematical programming.
• To match statistical moments between original and synthetic data without parametric assumptions.
• To evaluate the performance of this moment matching approach against existing methods like chained equations.

Main Methods:

• Developed a synthetic data generation technique leveraging linear and integer mathematical programming.
• Focused on matching moments (statistical properties) of the original data in the synthetic dataset.
• Applied the method to the Framingham Heart Study data and compared it with chained equations using Cox, logistic, and nonparametric models.

Main Results:

• Achieved 100% true coverage for parametric models (Cox, logistic regression) when matching up to four moments.
• The moment matching approach consistently outperformed the chained equations method for parametric models.
• Performance for nonparametric models was less stable; fourth-order moment matching showed benefits for parametric models but not consistently for nonparametric ones.

Conclusions:

• The proposed moment matching method is a viable alternative for synthetic data generation, particularly for parametric models.
• It offers no inherent disclosure risk and avoids distributional assumptions.
• The trade-off between benefits and computational costs for the moment matching approach should be considered.