Medical technologies such as imaging and sequencing make it possible to gather massive amounts of information at increasingly lower cost. Sharing data from studies can advance scientific understanding and improve healthcare outcomes. Concerns about patient privacy, however, can preclude open data sharing, thus hampering progress in understanding stigmatized conditions such as mental health disorders. Suppose there are several research groups studying a brain disorder (e.g. early-onset Alzheimers). They want to collaborate to see if they can learn common patterns in the MRI images from their research subjects. However, due to privacy concerns, each site wants to protect against the risk that someone could identify one of their research subjects.

This research seeks to understand how to analyze and learn from sensitive data held at different sites in a way that quantifiably and rigorously protects the privacy of the data. The framework used for this work is differential privacy, which measures the privacy risk when publishing information derived from sensitive data. We can guarantee privacy by providing only approximate answers, which means we trade off accuracy (or some other measure of utility) with privacy risk. In this project we looked at several different aspects of applying differential privacy to scenarios similar to the collaborative research example above. 

We first looked at the negative impact of differentally private approximations on utility. This impact is mitigated by more data; a larger sample size can enable better utility with lower privacy risk. Turning the question around, we ask: for a given desired level of privacy risk and utility, how much data do we need to meet both criteria? Comparing this to the amount of data needed when privacy is not a concern lets us quantify the cost of privacy in terms of the additional data needed. We looked at this cost in several illustrative but simple examples in a model of local differential privacy. This allowed us to understand if modeling assumptions can help improve the privacy-utility tradeoff.

A second branch of this work involved developing algorithms for decentralized learning and estimation using differential privacy. Here we focused on algorithms which try to estimate or factorize matrices that characterize the statistical structure of the underlying data. Some of the challenges involved in designing these methods are the potentially large number of messages that need to be exchanged, the total privacy risk and the quality of the result. This adds a third dimension (communication cost) to the privacy-utility tradeoff. When thinking about collaborative research projects, there are two points of comparison to evaluate these tradeoffs: one where a site simply uses its own data to perform the estimation (no collaboration, or a local solution) and one where the data from all sites is collected in one place (a global solution). This allows us to evaluate the cost of privacy, the cost of decentralization, and the benefits of collaboration.

The last part of this research involved putting the principles and ideas developed in the first two parts into practice. We worked with researchers in neuroimaging to implement and evaluate several of our methods, designing decentralized algorithms for key tasks in neuroimaging data processing pipelines. Through this process we also examined how some additional resources could enhance the privacy-utility tradeoff. In particular, we saw that if the sites could generate correlated random numbers, independent of the data, then we could achieve much better tradeoffs, sometimes as good as those for the global solution. We demonstrated this in a neuroimaging application to show that reasonable privacy-utility tradeoffs are possible when the consortium collectively has enough data.

Intellectual Merit: This proposal helped bridge the gap between the theory and practice of distributed privacy-preserving information processing. Overall, this project has led to a number of different insights around how privacy works in networked systems. In the intervening years, some of the models for decentralized estimaton have been rebranded as "federated learning." While we take medical research as a canonical example, this project encompasses many other application domains in which data holders wish to collaborate but have an oblication to protect the privacy of their data. We hope that some of the results developed in this project can inform the design of future privacy-preserving federated learning algorithms that can be applied to scientific collaborations.

Broader Impact: This work has directly informed the design of a collaborative research system for neuroimaging research. Evaluating algorithms within this system will lead to new insights in what the possible privacy-utility tradeoffs are for real data. The project supported several undergraduate students through diversity-focused REU programs, many of whom have gone on to successful graduate careers. Finally, this project resulted in tutorials for signal processing and machine learning audiences as well as a short course for statisticans on differential privacy to help bring differential privacy into statistical practice.

Last Modified: 11/18/2021
Modified by: Anand Sarwate