On Differentially Private Gaussian Hypothesis Testing

Data analysis for emerging systems such as syndromic surveillance or intelligent transportation systems requires testing statistical models based on privacy-sensitive data collected from individuals, e.g., medical records or location traces. In this paper, we design a differentially private hypothesis test based on the generalized likelihood ratio method to decide if data modeled as a sequence of independent and identically distributed Gaussian random variables has a given mean value. Analytic formulas for decision thresholds and for the test's receiver operating characteristic curve show explicitly the performance impact of the privacy constraint. We then apply the algorithm to the design of a differentially private anomaly (or fault) detector and study its performance for the analysis of a syndromic surveillance dataset from the Centers for Disease Control and Prevention in the United States.