Researchers Establish Fixed-Parameter Tractability for Private Synthetic Data Generation
A new theoretical paper establishes that generating synthetic data under differential privacy is fixed-parameter tractable (FPT) when the treewidth of the query family's incidence graph is used as the parameter. The work presents two algorithmic approaches—one based on linear programming and one on a subsampled private multiplicative weights method—both unified by dynamic programming over a tree decomposition. This result is significant because it provides the first provably efficient algorithms with optimal error rates for private synthetic data generation in a broad and practically relevant class of settings.
Researchers have established fixed-parameter tractability for the problem of generating synthetic data under differential privacy, with treewidth of the query family's incidence graph serving as the governing parameter. The paper presents two distinct algorithmic approaches: the first leverages linear programming and the FPT of the separation problem for the LP dual, while the second employs a subsampled private multiplicative weights method combined with FPT sampling from Gibbs distributions. Both approaches are unified under a dynamic programming framework operating over a tree decomposition of the query structure. The algorithms are shown to achieve optimal error rates across all parameter regimes, a notable theoretical guarantee. The work addresses a longstanding challenge in privacy-preserving machine learning, where generating high-quality synthetic data that satisfies differential privacy has been computationally difficult in general. By identifying treewidth as a tractable parameter, the results suggest that many real-world query families with low-treewidth structure can be handled efficiently. The paper was submitted to arXiv in June 2026 and spans both the algorithms and machine learning communities.
What's missing
As a preprint, this work has not yet undergone formal peer review. The paper does not appear to discuss empirical evaluations on real datasets, leaving open questions about practical performance and scalability beyond worst-case theoretical guarantees. It is also unclear how the treewidth parameter behaves for query families arising in common real-world applications, which would determine the practical scope of the tractability results.
What different sources said
- arXiv cs.LGCenter
Fixed-Parameter Tractability of Private Synthetic Data Generation
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