The Neural Hawkes Process: A Neurally Self-Modulating Multivariate Point Process
Many events occur in the world. Some event types are stochastically excited or inhibited-in the sense of having their probabilities elevated or decreased-by patterns in the sequence of previous events. Discovering such patterns can help us predict which type of event will happen next and when. We model streams of discrete events in continuous time, by constructing a neurally self-modulating multivariate point process in which the intensities of multiple event types evolve according to a novel continuous-time LSTM. This generative model allows past events to influence the future in complex and realistic ways, by conditioning future event intensities on the hidden state of a recurrent neural network that has consumed the stream of past events. Our model has desirable qualitative properties. It achieves competitive likelihood and predictive accuracy on real and synthetic datasets, including under missing-data conditions.
The proposed submission deals with an interesting and important problem: how to automatically learn the potentially complex temporal influence structures for the multivariate Hawkes process. The proposed neutrally self-modulating multivariate point process model can capture a range of superadditive, subadditive, or even subtractive influence structures from the historical events on the future event, and the model is quite flexible. Also, the model in evaluated on both the synthetic and the real data, and yields a competitive likelihood and prediction accuracy under missing data. 
Comments:
1.	Compared with existing work, one potential contribution of this submission is in the increased flexibility of the proposed model. First, in modeling the intensity function, a non-linear transfer function is introduced and is applied to the original defined intensity for multivariate Hawkes processes.  Second, it models the hidden state h(t) as a continuous-time LSTM.
2.	Since the model is more flexible and has more parameters to estimate, it will be harder to accurately learn the parameters. The algorithm basically follows the previous Back Propagation Through Time (Du et al, 2016) strategy and proposes using the Monte Carlo trick in evaluating the integral quantify in the likelihood. I think the convergence of the current algorithm might be very slow since they have too many parameters. Since the learning issue in this model is challenging, it is worthwhile discussing more on the computational efficiency. A more tractable and efficient learning algorithm might be needed in dealing with large-scale problems. 
3.	For the numerical section, only the likelihood under missing data is evaluated. It will be more convincing to add the results for the intensity accuracy evaluation.