Events that we observe in the world may be caused by other, unobserved events. We consider sequences of discrete events in continuous time. When only some of the events are observed, we propose particle smoothing to infer the missing events. Particle smoothing is an extension of particle filtering in which proposed events are conditioned on the future as well as the past. For our setting, we develop a novel proposal distribution that is a type of continuous-time bidirectional LSTM. We use the sampled particles in an approximate minimum Bayes risk decoder that outputs a single low-risk prediction of the missing events. We experiment in multiple synthetic and real domains, modeling the complete sequences in each domain with a neural Hawkes process (Mei & Eisner, 2017). On held-out incomplete sequences, our method is effective at inferring the ground-truth unobserved events. In particular, particle smoothing consistently improves upon particle filtering, showing the benefit of training a bidirectional proposal distribution.
The authors propose a particle smoothing approach with an approximate minimum Bayes risk decoder to impute missing events in the Neural Hawkes Process (NHP). The main goal is to address the missing events problem in continuous-time event analysis, which is an important problem in practice. The core idea is within the framework of particle smoothing. 
To formulate the posterior distribution of the missing event, the authors consider both the left-to-right past events and the right-to-left future events. The paper first applies the NHP to capture both the observed and inferred missing events to learn a representation of the past events, and then uses a similar NHP to learn the representation of the observed events from the future. Based on the two representations, it then formulates the intensity function of the missing events and uses the thinning algorithm to sample different particles. Based on the proposed distribution, the paper also considers to decode a single prediction achieving the Minimum Bayes Risk. Experiments on synthetic datasets with 10 different initializations and two real datasets show that the proposed smoothing approach is better than the filtering baseline. 
In general, this paper considers an important problem which is under active research in literature recently. However, there are a few weaknesses of the paper that should be addressed. 
1. The proposed technique is tightly connected to NHP, which could limit the applicability of the approach to other temporal point processes. The essential idea is similar to Bi-LSTM to learn the representation from both ends of a sequence of asynchronous temporal events. There are several different ways to represent the inter-event time to feed into the network other than NHP. Can the proposed method also be applied to other processes?
2. Within the particle filtering framework, each particle (hypothesis) is weighted by the likelihood of the sequence of observed events under that hypothesis. It turns out that the integral part of Equation 5 does not have an obvious analytical solution under NHP. Then, we first need a set of samples to approximate the likelihood evaluation. Later, we also need to sample particles. I am not quite convinced the computational efficiency of this approach in real applications of practice. Also, there is no analysis either empirically or analytically about the impact of the accumulative sampling errors on the inference performance. Furthermore, to learn the proposed distribution, the paper applies the REINFORCE algorithm under the proposed distribution q. But REINFORCE is known for large variance issue. Given that we already need lots of samples for the likelihood, it is unclear to me how stable the algorithm could be in practice.
3. The experimental evaluation is weak. For particle filtering and smoothing, it is known that the filtering techniques are candidates for solving the smoothing problem but perform poorly when T is large. That's why it is necessary to develop more sophisticated strategies for good smoothing
algorithms. As a result, it is unfair to only compare the smoothing approach with the filtering baseline. 
Actually, what people really care about is how different techniques can behave in real data to impute realistic missing events. From this perspective, I suggest to use the QQ-plot to evaluate the goodness of fitting on the synthetic dataset. For example, given a sequence of events generated from an independent temporal point process, we can randomly delete events, and then apply different techniques, including Linderman et al. (2017), Shelton et al.(2018), to impute missing events. Finally, we can compare the imputed sequence of events with the groundtruth. 
In addition, sequential monte carlo approach often suffers from skewed particle issue where one particle gradually dominates all the other particles with no diversity. It is unclear how the proposed approach is able to handle this. 
One missing related paper is "Learning Hawkes Processes from Short Doubly-Censored Event Sequences"
Section 5.2 can be significantly strengthened if comparing with at least one of these approaches.
4. The paper is fairly written. I had some trouble reading back and forth for understanding Figure 1 since it has long caption that is not self-contained. The annotation of Section 2 is also too heavy to quickly skim through to memorize.