Inferring Networks and Estimating Influence in Social Media

The propagation of information, cascading behavior, spread of ideas, viruses and diseases through a network have been studied in different contexts, such as viral marketing (Kempe et al., 2003), the spread of news and opinions (Adar et al., 2004), the spread of technological inovations (Rogers, 1999), and the spread of infectious diseases (Anderson et al., 1992). In such cases, we have a set of contagions diffusing across a network. As a contagion spreads in a network (static or dynamic) it creates a trace at that instant of time, called a cascade. In order to study network diffusion, there are usually two fundamental challenges that need to be addressed. First, to be able to track cascading processes of contagion diffusion, which is certainly nontrivial with large-real world graphs. For example, given data about when did which nodes get infected by a virus, one can construct an exponentially large number of trees containing the infected nodes consistent with the data and the exact inference problem is simply intractable. Second, in a typical scenario only the contamination of nodes as a function of time is observed and the structure of the diffusion network is often unknown or unobserved. For example, in a viral marketing setting, it is easy to track the products purchased by people with respect to time, but not who influenced them into purchasing those.