  Latent variable conditional models, including the latent conditional random
fields as a special case, are popular models for many natural language
processing and vision processing tasks. The computational complexity of the
exact decoding/inference in latent conditional random fields is unclear. In
this paper, we try to clarify the computational complexity of the exact
decoding. We analyze the complexity and demonstrate that it is an NP-hard
problem even on a sequential labeling setting. Furthermore, we propose the
latent-dynamic inference (LDI-Naive) method and its bounded version
(LDI-Bounded), which are able to perform exact-inference or
almost-exact-inference by using top-$n$ search and dynamic programming.
