200 research outputs found
Differentially Private Functional Summaries via the Independent Component Laplace Process
In this work, we propose a new mechanism for releasing differentially private
functional summaries called the Independent Component Laplace Process, or ICLP,
mechanism. By treating the functional summaries of interest as truly
infinite-dimensional objects and perturbing them with the ICLP noise, this new
mechanism relaxes assumptions on data trajectories and preserves higher utility
compared to classical finite-dimensional subspace embedding approaches in the
literature. We establish the feasibility of the proposed mechanism in multiple
function spaces. Several statistical estimation problems are considered, and we
demonstrate by slightly over-smoothing the summary, the privacy cost will not
dominate the statistical error and is asymptotically negligible. Numerical
experiments on synthetic and real datasets demonstrate the efficacy of the
proposed mechanism
New Directions for Contact Integrators
Contact integrators are a family of geometric numerical schemes which
guarantee the conservation of the contact structure. In this work we review the
construction of both the variational and Hamiltonian versions of these methods.
We illustrate some of the advantages of geometric integration in the
dissipative setting by focusing on models inspired by recent studies in
celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282
Differentially Private Synthetic Heavy-tailed Data
The U.S. Census Longitudinal Business Database (LBD) product contains
employment and payroll information of all U.S. establishments and firms dating
back to 1976 and is an invaluable resource for economic research. However, the
sensitive information in LBD requires confidentiality measures that the U.S.
Census in part addressed by releasing a synthetic version (SynLBD) of the data
to protect firms' privacy while ensuring its usability for research activities,
but without provable privacy guarantees. In this paper, we propose using the
framework of differential privacy (DP) that offers strong provable privacy
protection against arbitrary adversaries to generate synthetic heavy-tailed
data with a formal privacy guarantee while preserving high levels of utility.
We propose using the K-Norm Gradient Mechanism (KNG) with quantile regression
for DP synthetic data generation. The proposed methodology offers the
flexibility of the well-known exponential mechanism while adding less noise. We
propose implementing KNG in a stepwise and sandwich order, such that new
quantile estimation relies on previously sampled quantiles, to more efficiently
use the privacy-loss budget. Generating synthetic heavy-tailed data with a
formal privacy guarantee while preserving high levels of utility is a
challenging problem for data curators and researchers. However, we show that
the proposed methods can achieve better data utility relative to the original
KNG at the same privacy-loss budget through a simulation study and an
application to the Synthetic Longitudinal Business Database
- …