New proof makes private synthetic data generation tractable using treewidth
Two algorithms achieve optimal error by exploiting query structure, not just noise.
A team of researchers (Ghazi, Guzmán, Kamath, Knop, Kumar, Manurangsi) has established that generating synthetic data under differential privacy is fixed-parameter tractable when the parameter is the treewidth of the query family's incidence graph. This means the computational complexity grows polynomially in the data size, with exponential dependence only on a structural property of the queries—treewidth. The result is both theoretical and practical: the algorithms achieve optimal error rates across all regimes, a significant improvement over previous methods that often required exponential time or suboptimal accuracy.
The paper offers two distinct algorithmic realizations. The first leverages linear programming, showing that the separation problem for the LP dual is itself FPT, enabling efficient optimization even for complex query sets. The second uses a subsampled private multiplicative weights approach, where sampling from Gibbs distributions is made tractable via FPT techniques. Both methods are unified by a dynamic programming framework over a tree decomposition of the query incidence graph. For practitioners, this work opens the door to private synthetic data tools that can handle realistic query workloads—like range queries, marginal queries, or graph queries—without sacrificing either privacy or utility.
- Fixed-parameter tractability (FPT) achieved with treewidth of query incidence graph as the parameter
- Two algorithms: LP dual approach and subsampled private multiplicative weights with Gibbs sampling
- Optimal error rates guaranteed for all privacy regimes, with dynamic programming unifying both approaches
Why It Matters
Makes differentially private synthetic data generation practical for complex queries, balancing privacy, utility, and efficiency.