# Optimal Post-processing of Synthetic Data for Pearson Correlation Matching

arXiv: https://arxiv.org/abs/2510.02405 · HTML: https://mlsanity.com/paper/2510.02405/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 19 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Builds on (most cited first, 4 of 4)

- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [Post-processing Private Synthetic Data for Improving Utility on Selected Measures](https://mlsanity.com/paper/2305.15538/) (2023)
- [Data-Driven Time Series Reconstruction for Modern Power Systems Research](https://mlsanity.com/paper/2110.13772/) (2021)
- [Tunable correlation retention: A statistical method for generating synthetic data](https://mlsanity.com/paper/2403.01471/) (2024)

## Abstract (arXiv)

Preserving correlation in synthetic data is of interest in several applications. Existing approaches mainly address correlation preservation during the generation procedure. Here, we instead consider it as a postprocessing problem. Given original and synthetic tabular data, we seek the smallest change to the synthetic dataset that restores the Pearson correlation matrix of the original data. Under suitable assumptions, we derive a unique explicit solution to the minimization problem. We also provide a bound on the size of the correction in terms of the initial correlation error. On the numerical side, across several datasets and generation methods, the proposed approach largely preserves marginal distributions, t-SNE geometry, and classification performance. The method is generator-independent and can be applied after synthesis without modifying the generation procedure.