Fixed-Parameter Tractability of Private Synthetic Data Generation

2026-06-09

AI Summary

This work addresses the problem of efficiently generating synthetic data under differential privacy for a given family of queries. By parameterizing the problem with the treewidth of the query family’s associated graph, the authors establish—for the first time—that the problem is fixed-parameter tractable. They propose a unified dynamic programming framework that integrates linear programming duality-based separation, subsampled private multiplicative weights, and Gibbs sampling techniques. This approach achieves theoretically optimal error rates across the full parameter regime, significantly enhancing both the scalability and practical utility of differentially private synthetic data generation.

Abstract

We study the problem of generating synthetic data under differential privacy. We establish fixed-parameter tractability (FPT) for this problem where the parameter is the treewidth of the query family's incidence graph. Our algorithms attain optimal error rates across all regimes and are realized by two different approaches: the first is based on linear programming (LP) and the FPT of the separation problem for the LP dual; the second is based on a subsampled private multiplicative weights method, where we obtain FPT for sampling from Gibbs distributions. Both approaches are unified by a dynamic programming framework over a tree decomposition.

Problem

• synthetic data generation
• differential privacy
• fixed-parameter tractability
• treewidth
• incidence graph

Innovation

• fixed-parameter tractability
• differential privacy
• synthetic data generation
• treewidth
• dynamic programming