  Named entity recognition (NER) is a well-studied task in natural language
processing. However, the widely-used sequence labeling framework is difficult
to detect entities with nested structures. In this work, we view nested NER as
constituency parsing with partially-observed trees and model it with
partially-observed TreeCRFs. Specifically, we view all labeled entity spans as
observed nodes in a constituency tree, and other spans as latent nodes. With
the TreeCRF we achieve a uniform way to jointly model the observed and the
latent nodes. To compute the probability of partial trees with partial
marginalization, we propose a variant of the Inside algorithm, the
\textsc{Masked Inside} algorithm, that supports different inference operations
for different nodes (evaluation for the observed, marginalization for the
latent, and rejection for nodes incompatible with the observed) with efficient
parallelized implementation, thus significantly speeding up training and
inference. Experiments show that our approach achieves the state-of-the-art
(SOTA) F1 scores on the ACE2004, ACE2005 dataset, and shows comparable
performance to SOTA models on the GENIA dataset. Our approach is implemented
at: \url{https://github.com/FranxYao/Partially-Observed-TreeCRFs}.
