Computing Covariance and Correlation in Optimally Privacy-Protected Statistical Databases: Feasible Algorithms

Abstract

Abstract. In many real-life situations, e.g., in medicine, it is necessary to process data while preserving the patients' confidentiality. One of the most efficient methods of preserving privacy is to replace the exact values with intervals that contain these values. For example, instead of an exact age, a privacy-protected database only contains the information that the age is, e.g., between 10 and 20, or between 20 and 30, etc. Based on this data, it is important to compute correlation and covariance between different quantities. For privacy-protected data, different values from the intervals lead, in general, to different estimates for the desired statistical characteristic. Our objective is then to compute the range of possible values of these estimates. Algorithms for effectively computing such ranges have been developed for situations when intervals come from the original surveys, e.g., when a person fills in whether his or her age is between 10 or 20, between 20 and 30, etc. These intervals, however, do not always lead to an optimal privacy protection; it turns out that more complex, computer-generated "intervalization" can lead to better privacy under the same accuracy, or, alternatively, to more accurate estimates of statistical characteristics under the same privacy constraints. In this paper, we extend the existing efficient algorithms for computing covariance and correlation based on privacy-protected data to this more general case of interval data. Formulation of the ProblemNeed for processing data in statistical databases. Often, we collect data for the purpose of finding possible dependencies between different quantities. For example, we collect all possible information about the medical patients with the hope of finding out which factors affect different illnesses and which factors affect the success of different cures. The resulting collection of records r i = (r i1 , . . . , r ip ), 1 ≤ i ≤ n, is known as a statistical database since typically, statistical methods are used for look for possible dependencies; see, e.g., [7]. These statistical methods are usually based on computing statistical characteristics such as mean