Algorithms Achieve Fixed-Parameter Tractability for Differentially Private Synthetic Data Generation

Jul 16, 2026

A new preprint establishes that generating synthetic data under differential privacy is fixed-parameter tractable (FPT) when parameterized by the treewidth of the query family's incidence graph. The authors introduce two algorithms that achieve optimal error rates: one based on linear programming and the FPT of the LP dual's separation problem, and another using a subsampled private multiplicative weights method with FPT Gibbs sampling. Both approaches are unified by a dynamic programming framework over tree decompositions.

Why it matters: This result advances the theoretical understanding of private synthetic data generation, potentially enabling more efficient privacy-preserving data analysis for complex query families.

Full story at: arXiv Statistical ML ↗