Differentially Private Propensity Scores for Bias Correction

In surveys, it is typically up to the individuals to decide if they want to participate or not, which leads to participation bias: the individuals willing to share their data might not be representative of the entire population. Similarly, there are cases where one does not have direct access to any data of the target population and has to resort to publicly available proxy data sampled from a different distribution. In this paper, we present Differentially Private Propensity Scores for Bias Correction (DiPPS), a method for approximating the true data distribution of interest in both of the above settings. We assume that the data analyst has access to a dataset $\tilde{D}$ that was sampled from the distribution of interest in a biased way. As individuals may be more willing to share their data when given a privacy guarantee, we further assume that the analyst is allowed locally differentially private access to a set of samples $D$ from the true, unbiased distribution. Each data point from the private, unbiased dataset $D$ is mapped to a probability distribution over clusters (learned from the biased dataset $\tilde{D}$), from which a single cluster is sampled via the exponential mechanism and shared with the data analyst. This way, the analyst gathers a distribution over clusters, which they use to compute propensity scores for the points in the biased $\tilde{D}$, which are in turn used to reweight the points in $\tilde{D}$ to approximate the true data distribution. It is now possible to compute any function on the resulting reweighted dataset without further access to the private $D$. In experiments on datasets from various domains, we show that DiPPS successfully brings the distribution of the available dataset closer to the distribution of interest in terms of Wasserstein distance. We further show that this results in improved estimates for different statistics.