Nonparametric Multi-group Membership Model for Dynamic Networks
Relational data-like graphs, networks, and matrices-is often dynamic, where the relational structure evolves over time. A fundamental problem in the analysis of time-varying network data is to extract a summary of the common structure and the dynamics of the underlying relations between the entities. Here we build on the intuition that changes in the network structure are driven by dynamics at the level of groups of nodes. We propose a nonparametric multi-group membership model for dynamic networks. Our model contains three main components: We model the birth and death of individual groups with respect to the dynamics of the network structure via a distance dependent Indian Buffet Process. We capture the evolution of individual node group memberships via a Factorial Hidden Markov model. And, we explain the dynamics of the network structure by explicitly modeling the connectivity structure of groups. We demonstrate our model's capability of identifying the dynamics of latent groups in a number of different types of network data. Experimental results show that our model provides improved predictive performance over existing dynamic network models on future network forecasting and missing link prediction.
Nonparametric Multi-group Membership Model for Dynamic 
      Networks The paper proposes a new time varying multiple-membership 
      network model. The multiple group membership is modelled using an IBP 
      and the time evolution is modelled by a hidden Markov model. In 
      addition, groups can be born or die according to a stochastic process. 
      Modeling relational data using Bayesian nonparametrics has 
      recently received a lot of attention, and this paper makes a small but 
      significant step towards better modeling the dynamic behaviour of 
      evolving networks. In my mind, the proposed model makes 
      perfect sense as a general and very expressive model of time varying 
      networks. The only thing that I have some trouble understanding is the 
      argument for having the birth death process in the model. At every 
      time-step there are an infinite number of groups (according to the 
      IBP), and a finite number of the groups have members associated with 
      them. The HMMs tie these IBPs together, and if all members at some 
      point leave a group it will just be empty. Later, members can again 
      join this empty group (or join another empty group). These two 
      situations are disambiguated by the group parameters (link affinities) 
      so the inference will determine wheter a new group should be formed or 
      the old group should be "reused". The exact same is the case for the 
      model with the birth-death process, only this is a more complicated 
      model. Perhaps I misunderstand something? I think the paper is 
      very well written, and the argumentation (except the above mentioned) 
      was easy to follow. There is a nice balance between background 
      information, model specification, inference details, and experimental 
      validation. Some details regarding the inference is left out 
      (available in an extended version which I did not examine) and I think 
      this is a reasonable choice, since this is not essential for 
      understanding the main arguments. A few additional comments: 
      - The proposed model, like the LFRM model of Miller et al. [23] is 
      based on a logistic link function which is the reason that the 
      computational complexity of inference is at least N^2. I suspect 
      this prohibits the use of the proposed model to medium or large 
      scale network analysis. Using e.g. ideas in [24] the computational 
      complexity could be reduced significantly, which could be an 
      interesting topic of future research. - Is there any reason 
      why the density parameter epsilon is optimized rather than sampled? 
      - You might be interested in reading Herlau et al. Modeling 
      Temporal Evolution and Multiscale Structure in Networks, ICML 2013, 
      which is closely related to your work. I look forward to 
      hearing the authors' response to my comments. UPDATE: After 
      reading the authors' comments I stand by my assessment. Just to clarify, I 
      did not mean to say the use of the birth-death process was wrong, only 
      that I find this part of the model unnecessary and not very 
      elegant.