Relaxed Marginal Consistency for Differentially Private Query Answering

Many differentially private algorithms for answering database queries involve a step that reconstructs a discrete data distribution from noisy measurements. This provides consistent query answers and reduces error, but often requires space that grows exponentially with dimension. PRIVATE-PGM is a recent approach that uses graphical models to represent the data distribution, with complexity proportional to that of exact marginal inference in a graphical model with structure determined by the co-occurrence of variables in the noisy measurements. PRIVATE-PGM is highly scalable for sparse measurements, but may fail to run in high dimensions with dense measurements. We overcome the main scalability limitation of PRIVATE-PGM through a principled approach that relaxes consistency constraints in the estimation objective. Our new approach works with many existing private query answering algorithms and improves scalability or accuracy with no privacy cost. Differential Privacy Differential privacy protects individuals by bounding the impact any one individual can have on the output of an algorithm. Definition 1 (Differential Privacy [34] ). A randomized algorithm A satisfies ( , δ)-differential privacy if, for any input X, any X ∈ nbrs(X), and any subset of outputs S ⊆ Range(A), Above, nbrs(X) denotes the set of datasets formed by replacing any x (i) ∈ X with an arbitrary new record x (i) ∈ Ω. When δ = 0 we say A satisfies -differential privacy.