Paper:
COEVOLVE: A Joint Point Process Model for Information Diffusion and Network Co-evolution
Information diffusion in online social networks is affected by the underlying network topology, but it also has the power to change it. Online users are constantly creating new links when exposed to new information sources, and in turn these links are alternating the way information spreads. However, these two highly intertwined stochastic processes, information diffusion and network evolution, have been predominantly studied separately, ignoring their co-evolutionary dynamics. We propose a temporal point process model, COEVOLVE, for such joint dynamics, allowing the intensity of one process to be modulated by that of the other. This model allows us to efficiently simulate interleaved diffusion and network events, and generate traces obeying common diffusion and network patterns observed in real-world networks. Furthermore, we also develop a convex optimization framework to learn the parameters of the model from historical diffusion and network evolution traces. We experimented with both synthetic data and data gathered from Twitter, and show that our model provides a good fit to the data as well as more accurate predictions than alternatives.

Review:
This paper extends previous work on modeling network interactions with multivariate Hawkes processes by introducing a time-varying network into the model. For example, when one Twitter user publishes a tweet, followers of that user are likely to retweet in response. The dynamic network is intended to capture the creation of new connections, for example, when one Twitter user begins to follow another. The instantaneous network is represented by a binary adjacency matrix, and edges are added to the network according to a survival process with a event-driven rate. If one user frequently retweets another user's messages, then it is likely they will begin to follow that user and thereby add a new connection to the network. This combined modeling of activity and network evolution is captured in a joint probabilistic model, and inference is performed by maximum likelihood estimation.The problem is well-posed and elegantly solved. The paper could be strengthened by addressing a few concerns. First, it appears that the interaction weights ($\beta_s$'s) are shared by all interactions originating from source $s$. Intuitively, it seems that weights should instead be connection specific since the influence of a source node may vary from destination to destination. That is, it seems that $A$ should be accompanied by a weight matrix $W$. Second, this problem is conceptually related to the problem of inferring time-varying connection strengths given observations of spiking activity, which has received particular attention in the context of modeling neural synaptic plasticity. See Stevenson and Kording (NIPS 2011), Linderman, Stock, and Adams (NIPS 2014), and Song et. al. (J. Neuro. Meth. 2015). These papers model the evolution of a real-valued weight matrix rather than a binary adjacency matrix. Third, though in the context of Twitter it may be reasonable to assume that events are marked with their source and destination, in more general scenarios we may not observe the source. Your model could handle this scenario with the addition of latent variables for the unknown source, as in Simma and Jordan (UAI 2011). Notes: - The legend in Figure 6 says "Hawks" instead of "Hawkes"- "Twitter" and "Hawkes" should be capitalized in references - Linderman and Adams reference should be to ICML 2014 rather than arxiv* UPDATE * I appreciate the authors responses. I do think some of those clarifications/generalizations could be worthwhile additions to the paper.