Estimating the success of re-identifications in incomplete datasets using generative models.

While rich medical, behavioral, and socio-demographic data are key to modern data-driven research, their collection and use raise legitimate privacy concerns. Anonymizing datasets through de-identification and sampling before sharing them has been the main tool used to address those concerns. We here propose a generative copula-based method that can accurately estimate the likelihood of a specific person to be correctly re-identified, even in a heavily incomplete dataset. On 210 populations, our method obtains AUC scores for predicting individual uniqueness ranging from 0.84 to 0.97, with low false-discovery rate. Using our model, we find that 99.98% of Americans would be correctly re-identified in any dataset using 15 demographic attributes. Our results suggest that even heavily sampled anonymized datasets are unlikely to satisfy the modern standards for anonymization set forth by GDPR and seriously challenge the technical and legal adequacy of the de-identification release-and-forget model.

Local leaders in random networks.

We consider local leaders in random uncorrelated networks, i.e., nodes whose degree is higher than or equal to the degree of all their neighbors. An analytical expression is found for the probability for a node of degree k to be a local leader. This quantity is shown to exhibit a transition from a situation where high-degree nodes are local leaders to a situation where they are not, when the tail of the degree distribution behaves like the power law ~k(-gamma(c)) with gamma(c)=3 . Theoretical results are verified by computer simulations, and the importance of finite-size effects is discussed.

Distance distribution in random graphs and application to network exploration.

We consider the problem of determining the proportion of edges that are discovered in an Erdos-Rényi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of determining the proportion of edges connecting nodes that are at identical distance from the source node. The evolution of this quantity with the probability of existence of the edges exhibits intriguing oscillatory behavior. In order to perform our analysis, we introduce a different way of computing the distribution of distances between nodes. Our method outperforms previous similar analyses and leads to estimates that coincide remarkably well with numerical simulations. It allows us to characterize the phase transitions appearing when the connectivity probability varies.

Modelling Influence and Opinion Evolution in Online Collective Behaviour.

Opinion evolution and judgment revision are mediated through social influence. Based on a large crowdsourced in vitro experiment (n = 861), it is shown how a consensus model can be used to predict opinion evolution in online collective behaviour. It is the first time the predictive power of a quantitative model of opinion dynamics is tested against a real dataset. Unlike previous research on the topic, the model was validated on data which did not serve to calibrate it. This avoids to favor more complex models over more simple ones and prevents overfitting. The model is parametrized by the influenceability of each individual, a factor representing to what extent individuals incorporate external judgments. The prediction accuracy depends on prior knowledge on the participants' past behaviour. Several situations reflecting data availability are compared. When the data is scarce, the data from previous participants is used to predict how a new participant will behave. Judgment revision includes unpredictable variations which limit the potential for prediction. A first measure of unpredictability is proposed. The measure is based on a specific control experiment. More than two thirds of the prediction errors are found to occur due to unpredictability of the human judgment revision process rather than to model imperfection.