Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data
We propose a novel class of network models for temporal dyadic interaction data. Our objective is to capture important features often observed in social interactions: sparsity, degree heterogeneity, community structure and reciprocity. We use mutually-exciting Hawkes processes to model the interactions between each (directed) pair of individuals. The intensity of each process allows interactions to arise as responses to opposite interactions (reciprocity), or due to shared interests between individuals (community structure). For sparsity and degree heterogeneity, we build the non time dependent part of the intensity function on compound random measures following (Todeschini et al., 2016). We conduct experiments on realworld temporal interaction data and show that the proposed model outperforms competing approaches for link prediction, and leads to interpretable parameters.
Summary:  This work extends the Todeschini et al. (2016) framework for sparse community structure to a temporal Hawkes process network, and thus can capture both temporal reciprocity and community structure, which are properties often studied in (temporal) social interaction data. The framework is built on using compound CRMs, and then asymptotic properties of the model are described. Lastly, empirical results for link prediction, community structure, and power law distribution are presented on a variety of temporal social network datasets.  Strengths: - extends the static Todeschini et al. (2016) framework to a temporal setting, which has not been done before - Complex and flexible model for capturing sparsity, degree heterogeneity, and reciprocity, which are desirable properties for many real-world social networks with temporal structure — many existing models are either too simplistic (often ignoring temporal structure) - Develops an efficient inference algorithm for a complex model, and demonstrates on large network datasets - Well-written and good figures  Weaknesses: - Can be viewed as gluing together several existing components of network models: e.g., Caron&Fox and Todeschini et al., and Blundell et al. - Inference details are sparse, may be difficult to reproduce - Experiments are simplistic and applications  Quality:  The paper is technically correct. The claims of sparsity, heterogeneity, and community structure follow from the inherited random measure frameworks of Todeschini and Caron&Fox, and is sparsity (asymptotic) properties are also shown in Section 4.2. The self-excitation comes from the use of the Hawkes process.  The inference in the model appears to be quite scalable, as demonstrated on several large graphs. The model shows significant improvement on the link prediction task. Furthermore, it would be interesting to compare to (or even discuss more in depth) some of the more recent sparse graph models for temporal network data (e.g. Palla et al. and Ng&Silvea), which I don't believe incorporate reciprocity into the models.   The paper would benefit from more of a discussion on the strengths and weaknesses of this approach for modeling real-world temporal data. Currently, it does not appear that weaknesses are addressed.   The submission is clear and fairly well-written, and the figures are informative and intuitive, but in general, more details can be given as well as intuition on a dense topic.   Would be useful to the reader to motivate the 2-step inference procedure a bit further. For instance, the Jacob et al. paper was motivating the modular “cutting” with robustness and model misspecification. In addition, the paper should discuss the strengths and weaknesses of this inference approach.  Additionally, the inference section is a bit glossed-over in details. The current description is not the most useful for someone intending to implement the method from scratch, e.g., stating that MCMC and HMC were used is not sufficient. There is no discussion on the sensitivity of parameters and tuning that is often required. Though the inference is using an open-source package, the paper itself should include more thorough details for reproducibility purposes.  Originality & related work:  The main contribution of this paper is providing a new temporal network model that simultaneously captures sparsity, self-excitatory patterns, and community structure, and demonstrating inference on large graph data sets. However, all of these aspects can be viewed as a combination of well-known existing models for graphs (e.g., Caron--Fox, Todeschini et al., and Blundell et al.). The extension of the Caron--Fox and Todeschini et al. models to a temporal setting is novel, and very few models have approached this.   The related work is very thorough. (The bibliography should be checked for consistency and updated, e.g., Borgs et al. is now published, inconsistencies in the NIPS conference name, etc.)  Significance:  I’m unsure how useful the methods in this paper are for practical network modeling, and the paper may not add much additional value beyond existing work that models self-excitatory patterns in networks (e.g., the Blundell et al. paper). Though performed on large data sets, the experiments are toy experiments that don’t carefully study the data and application, and therefore the conclusions about the data are not particularly unique or surprising.   On the other hand, this is the first temporal version of the Caron--Fox framework that also includes latent community structure and also reciprocity, and could be viewed as a nice "first step" toward modeling temporal network data.   ---  Updated review:  Overall, I think the execution appears to be fairly strong, which is why I’d given it a weak accept score. I think that it is important to have new models of the relatively-new sparse graph frameworks this paper builds on that can be applied to real network data.  As this is a modeling and inference paper, the inference section needs to be able to be read on its own without referring to other work, and an honest assessment of the limitations of the model should be included. The experiments should go beyond just reporting prediction results (with error bars) and visualization of structure, and draw out the important insights of the data applications. The proofs in the appendix could also use more guiding descriptions.