A Formal Privacy Framework for Partially Private Data

Despite its many useful theoretical properties, differential privacy (DP) has one substantial blind spot: any release that non-trivially depends on confidential data without additional privacy-preserving randomization fails to satisfy DP. Such a restriction is rarely met in practice, as most data releases under DP are actually "partially private" data (PPD). This poses a significant barrier to accounting for privacy risk and utility under logistical constraints imposed on data curators, especially those working with official statistics. In this paper, we propose a privacy definition which accommodates PPD and prove it maintains similar properties to standard DP. We derive optimal transport-based mechanisms for releasing PPD that satisfy our definition and algorithms for valid statistical inference using PPD, demonstrating their improved performance over post-processing methods. Finally, we apply these methods to a case study on US Census and CDC PPD to investigate private COVID-19 infection rates. In doing so, we show how data curators can use our framework to overcome barriers to operationalizing formal privacy while providing more transparency and accountability to users.Comment: 31 pages, 7 figure

Non-linear transient heat conduction analysis of insulation wall of tank for transportation of liquid aluminum

This paper deals with transient non-linear heat conduction through the insulation wall of the tank for transportation of liquid aluminum. Tanks designed for this purpose must satisfy certain requirements regarding temperature of loading and unloading, duringtransport. Basic theoretical equations are presented, which describe the problem of heat conduction finite element analysis, starting from the differential equation of energy balance, taking into account the initial and boundary conditions of the problem. General 3-D problem for heat conduction is considered, from which solutions for two- and one-dimensional heat conduction can be obtained, as special cases. Forming of the finite element matrices using Galerkin method is briefly described. The procedure for solving equations of energy balance is discussed, by methods of resolving iterative processes of non-linear transient heat conduction. Solution of this problem illustrates possibilities of PAK-T software package, such as materials properties, given as tabular data, or analytical functions. Software alsooffers the possibility to solve non-linear and transient problems with incremental methods. Obtained results for different thicknesses of the tank wall insulation materials enable its comparison in regards to given conditions

Privacy-Preserving Data Sharing for Genome-Wide Association Studies

Traditional statistical methods for confidentiality protection of statistical databases do not scale well to deal with GWAS (genome-wide association studies) databases especially in terms of guarantees regarding protection from linkage to external information. The more recent concept of differential privacy, introduced by the cryptographic community, is an approach which provides a rigorous definition of privacy with meaningful privacy guarantees in the presence of arbitrary external information, although the guarantees come at a serious price in terms of data utility. Building on such notions, we propose new methods to release aggregate GWAS data without compromising an individual's privacy. We present methods for releasing differentially private minor allele frequencies, chi-square statistics and p-values. We compare these approaches on simulated data and on a GWAS study of canine hair length involving 685 dogs. We also propose a privacy-preserving method for finding genome-wide associations based on a differentially-private approach to penalized logistic regression