This paper investigates the relation between three different notions of privacy: identifiability, differential privacy and mutual-information privacy. Under a unified privacy-distortion framework, where the distortion is defined to be the Hamming distance of the input and output databases, we establish some fundamental connections between these three privacy notions. Given a distortion level @math , define @math to be the smallest (best) identifiability level, and @math to be the smallest differential privacy level. We characterize @math and @math , and prove that @math for @math in some range, where @math is a constant depending on the distribution of the original database @math , and diminishes to zero when the distribution of @math is uniform. Furthermore, we show that identifiability and mutual-information privacy are consistent in the sense that given distortion level @math , the mechanism that optimizes the mutual-information privacy also minimizes the identifiability level.
This is a paper about private data analysis, in which a trusted curator holding a confidential database responds to real vector-valued queries. A common approach to ensuring privacy for the database elements is to add appropriately generated random noise to the answers, releasing only these noisy responses. In this paper, we investigate various lower bounds on the noise required to maintain different kind of privacy guarantees. 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. In this work we provide efficient distributed protocols for generating shares of random noise, secure against malicious participants. The purpose of the noise generation is to create a distributed implementation of the privacy-preserving statistical databases described in recent papers [14,4,13]. In these databases, privacy is obtained by perturbing the true answer to a database query by the addition of a small amount of Gaussian or exponentially distributed random noise. The computational power of even a simple form of these databases, when the query is just of the form Σ i f(d i ), that is, the sum over all rows i in the database of a function f applied to the data in row i, has been demonstrated in [4]. A distributed implementation eliminates the need for a trusted database administrator. The results for noise generation are of independent interest. The generation of Gaussian noise introduces a technique for distributing shares of many unbiased coins with fewer executions of verifiable secret sharing than would be needed using previous approaches (reduced by a factor of n). The generation of exponentially distributed noise uses two shallow circuits: one for generating many arbitrarily but identically biased coins at an amortized cost of two unbiased random bits apiece, independent of the bias, and the other to combine bits of appropriate biases to obtain an exponential distribution. We introduce a new, generic framework for private data analysis.The goal of private data analysis is to release aggregate information about a data set while protecting the privacy of the individuals whose information the data set contains.Our framework allows one to release functions f of the data withinstance-based additive noise. That is, the noise magnitude is determined not only by the function we want to release, but also bythe database itself. One of the challenges is to ensure that the noise magnitude does not leak information about the database. To address that, we calibrate the noise magnitude to the smoothsensitivity of f on the database x --- a measure of variabilityof f in the neighborhood of the instance x. The new frameworkgreatly expands the applicability of output perturbation, a technique for protecting individuals' privacy by adding a smallamount of random noise to the released statistics. To our knowledge, this is the first formal analysis of the effect of instance-basednoise in the context of data privacy. Our framework raises many interesting algorithmic questions. Namely,to apply the framework one must compute or approximate the smoothsensitivity of f on x. We show how to do this efficiently for several different functions, including the median and the cost ofthe minimum spanning tree. We also give a generic procedure based on sampling that allows one to release f(x) accurately on manydatabases x. This procedure is applicable even when no efficient algorithm for approximating smooth sensitivity of f is known orwhen f is given as a black box. We illustrate the procedure by applying it to k-SED (k-means) clustering and learning mixtures of Gaussians.