The growing use of machine learning (ML) has raised concerns that an ML model may reveal private information about an individual who has contributed to the training dataset. To prevent leakage of sensitive data, we consider using differentially- private (DP), synthetic training data instead of real training data to train an ML model. A key desirable property of synthetic data is its ability to preserve the low-order marginals of the original distribution. Our main contribution comprises novel upper and lower bounds on the excess empirical risk of linear models trained on such synthetic data, for continuous and Lipschitz loss functions. We perform extensive experimentation alongside our theoretical results.

The grid file is a well known access method for multi-dimensional and spatial data. The response time needed to process path and range queries on the grid file access method can be improved significantly by distributing the data pages over multiple disks. The paper explores the disk allocation methods used to allocate the data pages of grid file among a set of disks, which can be accessed in parallel. Given N disks, a perfect allocation will speed up the processing of each query by a factor of N in this environment. The authors show that no disk allocation is perfect for the set of all orthogonal range queries, even on uniformly distributed read-only data. They then introduce two families of allocation methods, namely the Linear allocation method and the Lattice allocation method, which are perfect for a large collection of interesting path queries (rows, columns, diagonals, anti-diagonals) and range queries (small rectangles), on an interesting set of data distributions. They address the issues in extending disk allocation methods to general data distributions with random updates. Finally, they provide experimental results on the performance of the proposed methods and other well known disk allocation methods on different query sets, data distributions and data set sizes.>