Differential privacy with compression

This work studies formal utility and privacy guarantees for a simple multiplicative database transformation, where the data are compressed by a random linear or affine transformation, reducing the number of data records substantially, while preserving the number of original input variables.We provide an analysis framework inspired by a recent concept known as differential privacy. Our goal is to show that, despite the general difficulty of achieving the differential privacy guarantee, it is possible to publish synthetic data that are useful for a number of common statistical learning applications. This includes high dimensional sparse regression, principal component analysis (PCA), and other statistical measures based on the covariance of the initial data.