  We present an approach to differentially private computation in which one
does not scale up the magnitude of noise for challenging queries, but rather
scales down the contributions 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.
