On Conditional Correlations

The Pearson correlation, correlation ratio, and maximal correlation have been well-studied in the literature. In this paper, we study the conditional versions of these quantities. We extend the most important properties of the unconditional versions to the conditional versions, and also derive some new properties. Based on the conditional maximal correlation, we define an information-correlation function of two arbitrary random variables, and use it to derive an impossibility result for the problem of the non-interactive simulation of random variables.Comment: 20 pages. The application of our results on conditional correlations to the non-interactive simulation problem was adde

Data Disclosure under Perfect Sample Privacy

Perfect data privacy seems to be in fundamental opposition to the economical and scientific opportunities associated with extensive data exchange. Defying this intuition, this paper develops a framework that allows the disclosure of collective properties of datasets without compromising the privacy of individual data samples. We present an algorithm to build an optimal disclosure strategy/mapping, and discuss it fundamental limits on finite and asymptotically large datasets. Furthermore, we present explicit expressions to the asymptotic performance of this scheme in some scenarios, and study cases where our approach attains maximal efficiency. We finally discuss suboptimal schemes to provide sample privacy guarantees to large datasets with a reduced computational cost.Comment: 34 pages, 6 Figures, 1 Tabl