Generative Correlation Manifolds: Generating Synthetic Data with Preserved Higher-Order Correlations

TL;DR

This paper introduces Generative Correlation Manifolds (GCM), a novel method for creating synthetic data that accurately preserves complex correlation structures, including higher-order interactions, to improve data utility and privacy.

Contribution

The paper presents GCM, a computationally efficient technique that mathematically guarantees preservation of the full correlation structure in synthetic data generation.

Findings

GCM accurately preserves higher-order correlations.

Synthetic data maintains complex multi-variable interactions.

Method is computationally efficient and scalable.

Abstract

The increasing need for data privacy and the demand for robust machine learning models have fueled the development of synthetic data generation techniques. However, current methods often succeed in replicating simple summary statistics but fail to preserve both the pairwise and higher-order correlation structure of the data that define the complex, multi-variable interactions inherent in real-world systems. This limitation can lead to synthetic data that is superficially realistic but fails when used for sophisticated modeling tasks. In this white paper, we introduce Generative Correlation Manifolds (GCM), a computationally efficient method for generating synthetic data. The technique uses Cholesky decomposition of a target correlation matrix to produce datasets that, by mathematical proof, preserve the entire correlation structure -- from simple pairwise relationships to higher-order interactions -- of the source dataset. We argue that this method provides a new approach to synthetic data generation with potential applications in privacy-preserving data sharing, robust model training, and simulation.