Abstract: In light of big data and powerful machine learning algorithms that can quickly search and analyze large amounts of data, issues of data privacy protection are becoming more pressing than ever before. An increasingly popular approach towards data privacy protection, which is robust against any kind of adversary, is the notion of `differential privacy’. Although nowadays differential privacy receives a lot of attention also from within the statistics community, still even some of the most basic questions appear to be open.

In this talk we begin with a very general introduction to privacy aware data analysis via differential privacy. We then turn to the local paradigm of differential privacy and focus on the classical statistical problem of efficient estimation in regular parametric models. We highlight some of the intricacies that appear when the classical theory is adapted to procedures that guarantee local differential privacy and propose a general solution for the single parameter case. At the core of the new theory lies a challenging optimization problem for which efficient algorithms are sorely needed. Most of this talk is work in progress.

Abstract: When a decision, such as the approval or denial of bank loan, is delegated to a computer, an explanation of that decision ought to be given with it. This ethical need to explain the decisions leads to the search for a formal definition of the notion of explanation. This question meets older questions in logic regarding the explanatory nature of proof.