Yiming Paul Li

Mahnush Movahedi, Benjamin M. Case, Andrew Knox et al.

In this paper, we outline a way to deploy a privacy-preserving protocol for multiparty Randomized Controlled Trials on the scale of 500 million rows of data and more than a billion gates. Randomized Controlled Trials (RCTs) are widely used to improve business and policy decisions in various sectors such as healthcare, education, criminology, and marketing. A Randomized Controlled Trial is a scientifically rigorous method to measure the effectiveness of a treatment. This is accomplished by randomly allocating subjects to two or more groups, treating them differently, and then comparing the outcomes across groups. In many scenarios, multiple parties hold different parts of the data for conducting and analyzing RCTs. Given privacy requirements and expectations of each of these parties, it is often challenging to have a centralized store of data to conduct and analyze RCTs. We accomplish this by a three-stage solution. The first stage uses the Private Secret Share Set Intersection (PS$^3$I) solution to create a joined set and establish secret shares without revealing membership, while discarding individuals who were placed into more than one group. The second stage runs multiple instances of a general purpose MPC over a sharded database to aggregate statistics about each experimental group while discarding individuals who took an action before they received treatment. The third stage adds distributed and calibrated Differential Privacy (DP) noise to the aggregate statistics and uncertainty measures, providing formal two-sided privacy guarantees. We also evaluate the performance of multiple open source general purpose MPC libraries for this task. We additionally demonstrate how we have used this to create a working ads effectiveness measurement product capable of measuring hundreds of millions of individuals per experiment.

Jingang Miao, Yiming Paul Li

The ratio of two Gaussians is useful in many contexts of statistical inference. We discuss statistically valid inference of the ratio under Differential Privacy (DP). We use the delta method to derive the asymptotic distribution of the ratio estimator and use the Gaussian mechanism to provide (epsilon, delta)-DP guarantees. Like many statistics, quantities involved in the inference of a ratio can be re-written as functions of sums, and sums are easy to work with for many reasons. In the context of DP, the sensitivity of a sum is easy to calculate. We focus on getting the correct coverage probability of 95\% confidence intervals (CIs) of the DP ratio estimator. Our simulations show that the no-correction method, which ignores the DP noise, gives CIs that are too narrow to provide proper coverage for small samples. In our specific simulation scenario, the coverage of 95% CIs can be as low as below 10%. We propose two methods to mitigate the under-coverage issue, one based on Monte Carlo simulation and the other based on analytical correction. We show that the CIs of our methods have much better coverage with reasonable privacy budgets. In addition, our methods can handle weighted data, when the weights are fixed and bounded.