A rigorous foundational approach to private data analysis has emerged in theoretical computer science in the last decade, with differential privacy and its close variants playing a central role. We have recently been able to train complex machine learning models with little accuracy loss, while giving strong differentially privacy guarantees. The analyses of these algorithms rely on a class of results known as privacy amplification theorems. In this talk, I will sketch how private ML models can be trained, and how they can be analysed. I will then describe two recent privacy amplification theorems, and some of their implications.

(Joint works with Ulfar Erlingsson, Vitaly Feldman, Ilya Mironov, Ananth Raghunathan and  Abhradeep Thakurta)