The question is anything but abstract. Whether you’re streaming TV shows in the evening, shopping online, or at the hospital: Machine learning models have long been used everywhere. In doing so, they process highly sensitive data: Our social media posts are scanned, our health data is analyzed, and our interactions with chatbots are fed back into the training of the models. All this data provides deep insights into our behavior and our living conditions. This makes the question of how the effective use of ML models can be reconciled with the protection of our privacy all the more urgent. This is precisely the area where our new CISPA-Faculty Dr. Andrew Lowy is working: “Above all, I ask myself: What is the best possible performance we can hope for from a model when we also take aspects like privacy or robustness into account?”
Know Your Limits—This Also Applies to Machine Learning
In his work, Lowy investigates how good learning algorithms can fundamentally be under privacy and fairness requirements and develops methods that achieve these theoretical performance limits as efficiently as possible in practice. “If you don’t know the fundamental limits, an entire research community might end up wasting years trying to improve something that’s already optimal.” This is where his work comes in: He develops methods while simultaneously analyzing their theoretical performance. “I prove both upper and lower bounds, so I show what is achievable and what is impossible.” This focus on so-called “fundamental limits” is strongly influenced by classical methods from statistics and information theory, which Lowy applies to modern problems in machine learning.
Accuracy Versus Privacy: The Trade-Off Must Be Right
A fundamental tension arises between the accuracy of models, the protection of privacy, and their efficiency. “When we use techniques to protect personal data while training models, these often reduce the quantity or quality of the data available to a model,” explains Lowy.
A central approach in this context is so-called differential privacy. This is based on a strictly mathematical definition of data protection: It guarantees that individual data points have only a very limited influence on the outcome of an analysis. In practice, this is achieved by intentionally making results slightly “blurred” through small random deviations that obscure individual contributions without significantly distorting the overall picture.
Large companies like Apple or Google are already using differential privacy in specific applications. At the same time, its implementation remains challenging. “Differential privacy remains the gold standard when it comes to protecting privacy,” says Lowy. “But you can’t simply ‘make an algorithm private’ and expect it to work well.” Determining how much uncertainty can be introduced without losing the significance of the results requires precise calibration.
Learning Without a Central Authority
In addition to traditional scenarios, Lowy also focuses on federated learning. These are approaches where data remains decentralized and models are trained collaboratively. Such methods are used, for example, with sensitive medical data: Hospitals do not have to share their data or make it centrally available, yet everyone benefits from the insights that can be derived from patient data.
Here, the requirements for data protection are also shifting: “In federated learning, traditional differential privacy is often insufficient.” Instead, stronger guarantees are needed that also safeguard the exchange between different parties. Lowy’s work demonstrates how such models can be formally defined and algorithmically implemented. This is an important step for applications where data cannot or should not be collected centrally.
Open Problems and Next Steps
Despite significant progress, Lowy believes his field of research is still far from reaching its goal. Particularly in the area of modern neural networks—that is, non-convex optimization problems—many fundamental questions remain unresolved. “Current algorithms for deep learning are far from optimal.” It is precisely here that he sees great potential for future research and the opportunity to bring theory and practice even closer together.
The Beauty of Mathematics
Lowy’s own path into research was not a straight one: Originally, the American studied public policy with a focus on economics at Princeton University before finding his way to machine learning via mathematics. “I fell in love with mathematics when I realized how many challenges it holds,” he says. This enthusiasm for fundamental questions continues to shape his work today: the interest not only in developing solutions, but in understanding what is fundamentally possible and what is not.
