Tomography of the London Underground: a Scalable Model for Origin-Destination Data
The paper addresses the classical network tomography problem of inferring local traffic given origin-destination observations. Focusing on large complex public transportation systems, we build a scalable model that exploits input-output information to estimate the unobserved link/station loads and the users' path preferences. Based on the reconstruction of the users' travel time distribution, the model is flexible enough to capture possible different path-choice strategies and correlations between users travelling on similar paths at similar times. The corresponding likelihood function is intractable for medium or large-scale networks and we propose two distinct strategies, namely the exact maximum-likelihood inference of an approximate but tractable model and the variational inference of the original intractable model. As an application of our approach, we consider the emblematic case of the London underground network, where a tap-in/tap-out system tracks the starting/exit time and location of all journeys in a day. A set of synthetic simulations and real data provided by Transport For London are used to validate and test the model on the predictions of observable and unobservable quantities.
I thank the authors for the clarification in their rebuttal. It is even more clear that the authors should better contrast their work with aggregate approaches such as Dan Sheldon's collective graphical models (e.g., Sheldon and Dietterich (2011), Kumar et al. 2013, Bernstein and Sheldon 2016). 
Part of the confusion came from some of the modeling choices: In equation (1) the travel times added by one station is Poisson distributed?! Poisson is often used for link loads (how many people there are in a given station), not to model time. Is the quantization of time too coarse for a continuous-time model? Treating time as a Poisson r.v. requires some justification. Wouldn't a phase-type distribution(e.g., Erlang)  be a better choice for time? Such modeling choices must be explained.
The main problem, I fear, is not in the technical details. The paper is missing a bigger insight into inferring traffic loads from OD pairs. Something beyond solving this particular problem as a mixture of Poissons with path constraints. 
It is important to emphasize that the evaluation is not predictive (of the future) but rather it gives estimates of hidden variables. It is a transductive method as it cannot predict anything beyond the time horizon given in the training data. I am OK with that.
Figure 4 is missing a simple baseline using the shortest paths.
The results of the model in Figure 5 don't seem to match the data in the smaller stations (e.g., Finchley Road).
Minor comments:
What is the difference between the distributions Poisson and poisson in eqs (7) and (9)?
Figure 3: botton => bottom
      A. Kumar, D. Sheldon, and B. Srivastava. 2013. Collective Diffusion over Networks: Models and Inference. In Proceedings of International Conference on Uncertainty in Artificial Intelligence. 351–360.
      Garrett Bernstein, Daniel Sheldon,Consistently Estimating Markov Chains with Noisy Aggregate Data, AISTATS, 2016.
      Du, J., Kumar, A., and Varakantham, P. (2014, May). On understanding diffusion dynamics of patrons at a theme park. In Proceedings of the 2014 international conference on Autonomous agents and multi-agent systems (pp. 1501-1502). International Foundation for Autonomous Agents and Multiagent Systems.