Learning from Mixtures of Private and Public Populations
This addresses privacy-preserving machine learning for scenarios like medical studies where sensitive and non-sensitive data are mixed, offering a novel approach beyond prior homogeneous assumptions.
The paper tackles the problem of supervised learning with differential privacy constraints when data comes from a mixture of private and public sub-populations with potentially different distributions, focusing on learning linear classifiers. It shows that in cases where privacy status correlates with labels, linear classifiers can be learned with sample complexity comparable to non-private PAC-learning, which is impossible if all data is private.
We initiate the study of a new model of supervised learning under privacy constraints. Imagine a medical study where a dataset is sampled from a population of both healthy and unhealthy individuals. Suppose healthy individuals have no privacy concerns (in such case, we call their data "public") while the unhealthy individuals desire stringent privacy protection for their data. In this example, the population (data distribution) is a mixture of private (unhealthy) and public (healthy) sub-populations that could be very different. Inspired by the above example, we consider a model in which the population $\mathcal{D}$ is a mixture of two sub-populations: a private sub-population $\mathcal{D}_{\sf priv}$ of private and sensitive data, and a public sub-population $\mathcal{D}_{\sf pub}$ of data with no privacy concerns. Each example drawn from $\mathcal{D}$ is assumed to contain a privacy-status bit that indicates whether the example is private or public. The goal is to design a learning algorithm that satisfies differential privacy only with respect to the private examples. Prior works in this context assumed a homogeneous population where private and public data arise from the same distribution, and in particular designed solutions which exploit this assumption. We demonstrate how to circumvent this assumption by considering, as a case study, the problem of learning linear classifiers in $\mathbb{R}^d$. We show that in the case where the privacy status is correlated with the target label (as in the above example), linear classifiers in $\mathbb{R}^d$ can be learned, in the agnostic as well as the realizable setting, with sample complexity which is comparable to that of the classical (non-private) PAC-learning. It is known that this task is impossible if all the data is considered private.