Strongly universally consistent nonparametric regression and classification with privatised data

In recent years there has been a surge of interest in data analysis methodology that is able to achieve strong statistical performance without comprimising the privacy and security of individual data holders. This has often been driven by applications in modern technology, for example by Google (Erlingsson et al., 2014), Apple (Tang et al., 2017), and Microsoft (Ding et al., 2017), but the study goes at least as far back as Warner (1965) and is often used in more traditional fields of clinical trials (Vu and Slavkovic, 2009, Dankar and El Emam, 2013) and census data (Machanavajjhala et al., 2008, Dwork, 2019). While there has long been an awareness that sensitive data must be anonymised, it has become apparent only relatively recently that simply removing names and addresses is insufficient in many cases (e.g.