The power of A/B testing under interference

In this paper, we address the fundamental statistical question: how can you assess the power of an A/B test when the units in the study are exposed to interference? This question is germane to many scientific and industrial practitioners that rely on A/B testing in environments where control over interference is limited. We begin by proving that interference has a measurable effect on its sensitivity, or power. We quantify the power of an A/B test of equality of means as a function of the number of exposed individuals under any interference mechanism. We further derive a central limit theorem for the number of exposed individuals under a simple Bernoulli switching interference mechanism. Based on these results, we develop a strategy to estimate the power of an A/B test when actors experience interference according to an observed network model. We demonstrate how to leverage this theory to estimate the power of an A/B test on units sharing any network relationship, and highlight the utility of our method on two applications - a Facebook friendship network as well as a large Twitter follower network. These results yield, for the first time, the capacity to understand how to design an A/B test to detect, with a specified confidence, a fixed measurable treatment effect when the A/B test is conducted under interference driven by networks.Comment: 14 page

Message-Passing Methods for Complex Contagions

Message-passing methods provide a powerful approach for calculating the expected size of cascades either on random networks (e.g., drawn from a configuration-model ensemble or its generalizations) asymptotically as the number $N$ of nodes becomes infinite or on specific finite-size networks. We review the message-passing approach and show how to derive it for configuration-model networks using the methods of (Dhar et al., 1997) and (Gleeson, 2008). Using this approach, we explain for such networks how to determine an analytical expression for a "cascade condition", which determines whether a global cascade will occur. We extend this approach to the message-passing methods for specific finite-size networks (Shrestha and Moore, 2014; Lokhov et al., 2015), and we derive a generalized cascade condition. Throughout this chapter, we illustrate these ideas using the Watts threshold model.Comment: 14 pages, 3 figure

Dynamical Systems on Networks: A Tutorial

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than original version, some reorganization and also more pointers to interesting direction

The role of bot squads in the political propaganda on Twitter

Social Media are nowadays the privileged channel for information spreading and news checking. Unexpectedly for most of the users, automated accounts, also known as social bots, contribute more and more to this process of news spreading. Using Twitter as a benchmark, we consider the traffic exchanged, over one month of observation, on a specific topic, namely the migration flux from Northern Africa to Italy. We measure the significant traffic of tweets only, by implementing an entropy-based null model that discounts the activity of users and the virality of tweets. Results show that social bots play a central role in the exchange of significant content. Indeed, not only the strongest hubs have a number of bots among their followers higher than expected, but furthermore a group of them, that can be assigned to the same political tendency, share a common set of bots as followers. The retwitting activity of such automated accounts amplifies the presence on the platform of the hubs' messages.Comment: Under Submissio