  Extracting event temporal relations is a critical task for information
extraction and plays an important role in natural language understanding. Prior
systems leverage deep learning and pre-trained language models to improve the
performance of the task. However, these systems often suffer from two
short-comings: 1) when performing maximum a posteriori (MAP) inference based on
neural models, previous systems only used structured knowledge that are assumed
to be absolutely correct, i.e., hard constraints; 2) biased predictions on
dominant temporal relations when training with a limited amount of data. To
address these issues, we propose a framework that enhances deep neural network
with distributional constraints constructed by probabilistic domain knowledge.
We solve the constrained inference problem via Lagrangian Relaxation and apply
it on end-to-end event temporal relation extraction tasks. Experimental results
show our framework is able to improve the baseline neural network models with
strong statistical significance on two widely used datasets in news and
clinical domains.
