  Events in the world may be caused by other, unobserved events. We consider
sequences of events in continuous time. Given a probability model of complete
sequences, we propose particle smoothing---a form of sequential importance
sampling---to impute the missing events in an incomplete sequence. We develop a
trainable family of proposal distributions based on a type of bidirectional
continuous-time LSTM: Bidirectionality lets the proposals condition on future
observations, not just on the past as in particle filtering. Our method can
sample an ensemble of possible complete sequences (particles), from which we
form a single consensus prediction that has low Bayes risk under our chosen
loss metric. We experiment in multiple synthetic and real domains, using
different missingness mechanisms, and 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, with particle smoothing consistently improving upon particle filtering.
