On the Differential Privacy of Bayesian Inference

We study how to communicate findings of Bayesian inference to third parties, while preserving the strong guarantee of differential privacy. Our main contributions are four different algorithms for private Bayesian inference on proba-bilistic graphical models. These include two mechanisms for adding noise to the Bayesian updates, either directly to the posterior parameters, or to their Fourier transform so as to preserve update consistency. We also utilise a recently introduced posterior sampling mechanism, for which we prove bounds for the specific but general case of discrete Bayesian networks; and we introduce a maximum-a-posteriori private mechanism. Our analysis includes utility and privacy bounds, with a novel focus on the influence of graph structure on privacy. Worked examples and experiments with Bayesian na{\"i}ve Bayes and Bayesian linear regression illustrate the application of our mechanisms.Comment: AAAI 2016, Feb 2016, Phoenix, Arizona, United State

Prediction, evolution and privacy in social and affiliation networks

In the last few years, there has been a growing interest in studying online social and affiliation networks, leading to a new category of inference problems that consider the actor characteristics and their social environments. These problems have a variety of applications, from creating more effective marketing campaigns to designing better personalized services. Predictive statistical models allow learning hidden information automatically in these networks but also bring many privacy concerns. Three of the main challenges that I address in my thesis are understanding 1) how the complex observed and unobserved relationships among actors can help in building better behavior models, and in designing more accurate predictive algorithms, 2) what are the processes that drive the network growth and link formation, and 3) what are the implications of predictive algorithms to the privacy of users who share content online. The majority of previous work in prediction, evolution and privacy in online social networks has concentrated on the single-mode networks which form around user-user links, such as friendship and email communication. However, single-mode networks often co-exist with two-mode affiliation networks in which users are linked to other entities, such as social groups, online content and events. We study the interplay between these two types of networks and show that analyzing these higher-order interactions can reveal dependencies that are difficult to extract from the pair-wise interactions alone. In particular, we present our contributions to the challenging problems of collective classification, link prediction, network evolution, anonymization and preserving privacy in social and affiliation networks. We evaluate our models on real-world data sets from well-known online social networks, such as Flickr, Facebook, Dogster and LiveJournal