Causal Inference with Differentially Private (Clustered) Outcomes
Adel Javanmard Vahab Mirrokni Jean Pouget-Abadie
Estimating causal effects from randomized experiments is only feasible if
participants agree to reveal their potentially sensitive responses. Of the many
ways of ensuring privacy, label differential privacy is a widely used measure
of an algorithm's privacy guarantee, which might encourage participants to
share responses without running the risk of de-anonymization. Many
differentially private mechanisms inject noise into the original data-set to
achieve this privacy guarantee, which increases the variance of most
statistical estimators and makes the precise measurement of causal effects
difficult: there exists a fundamental privacy-variance trade-off to performing
causal analyses from differentially private data. With the aim of achieving
lower variance for stronger privacy guarantees, we suggest a new differential
privacy mechanism, "Cluster-DP", which leverages any given cluster structure of
the data while still allowing for the estimation of causal effects. We show
that, depending on an intuitive measure of cluster quality, we can improve the
variance loss while maintaining our privacy guarantees. We compare its
performance, theoretically and empirically, to that of its unclustered version
and a more extreme uniform-prior version which does not use any of the original
response distribution, both of which are special cases of the "Cluster-DP"
algorithm.