  Traditional structured prediction models try to learn the conditional
likelihood, i.e., p(y|x), to capture the relationship between the structured
output y and the input features x. For many models, computing the likelihood is
intractable. These models are therefore hard to train, requiring the use of
surrogate objectives or variational inference to approximate likelihood. In
this paper, we propose conditional Glow (c-Glow), a conditional generative flow
for structured output learning. C-Glow benefits from the ability of flow-based
models to compute p(y|x) exactly and efficiently. Learning with c-Glow does not
require a surrogate objective or performing inference during training. Once
trained, we can directly and efficiently generate conditional samples. We
develop a sample-based prediction method, which can use this advantage to do
efficient and effective inference. In our experiments, we test c-Glow on five
different tasks. C-Glow outperforms the state-of-the-art baselines in some
tasks and predicts comparable outputs in the other tasks. The results show that
c-Glow is versatile and is applicable to many different structured prediction
problems.
