Calibrating Data to Sensitivity in Private Data Analysis A Platform for Differentially-Private Analysis of Weighted Datasets. Full version. Last updated February 14, 2014.

We present an approach to differentially private computa-tion in which one does not scale up the magnitude of noise for challenging queries, but rather scales down the contribu-tions of challenging records. While scaling down all records uniformly is equivalent to scaling up the noise magnitude, we show that scaling records non-uniformly can result in substantially higher accuracy by bypassing the worst-case requirements of differential privacy for the noise magnitudes. This paper details the data analysis platform wPINQ, which generalizes the Privacy Integrated Query (PINQ) to weighted datasets. Using a few simple operators (including a non-uniformly scaling Join operator) wPINQ can reproduce (and improve) several recent results on graph analysis and introduce new generalizations (e.g., counting triangles with given degrees). We also show how to integrate probabilistic inference techniques to synthesize datasets respecting more complicated (and less easily interpreted) measurements. 1