Publications

Existing private methods for estimating density modes mainly recover a single mode, while recovering all modes requires searches from multiple starting locations that can themselves reveal information about individual records. We propose DP-GRAMS, a differentially private algorithm that selects starting locations with a density-aware initialization on a public grid, moves each toward higher estimated density, and groups the endpoints into estimated modes, all within a single privacy budget. We prove that DP-GRAMS satisfies differential privacy and recovers every population mode with high probability, with error bounds that separate statistical error from the cost of privacy and a lower bound showing these rates are nearly optimal. We extend the method to modal regression and clustering and show that it preserves tumor-type separation in cancer gene-expression data.

Our Google Summer of Code project “Improvements to nls ()” investigated rationalizing R tools for nonlinear regression and nonlinear estimation tools by considering usability, maintainability, and functionality, especially for a Gauss-Newton solver. The rich features of nls () are weakened by several deficiencies and inconsistencies such as a lack of stabilization of the Gauss-Newton solver. Further considerations are the usability and maintainability of the code base that provides the functionality nls () claims to offer. Various packages, including our nlsr, provide alternative capabilities. We consider the differences in goals, approaches, and features of different tools for nonlinear least squares modeling in R. Discussion of these matters is relevant to improving R generally as well as its nonlinear estimation tools.