  Self-training has proven effective for improving NMT performance by
augmenting model training with synthetic parallel data. The common practice is
to construct synthetic data based on a randomly sampled subset of large-scale
monolingual data, which we empirically show is sub-optimal. In this work, we
propose to improve the sampling procedure by selecting the most informative
monolingual sentences to complement the parallel data. To this end, we compute
the uncertainty of monolingual sentences using the bilingual dictionary
extracted from the parallel data. Intuitively, monolingual sentences with lower
uncertainty generally correspond to easy-to-translate patterns which may not
provide additional gains. Accordingly, we design an uncertainty-based sampling
strategy to efficiently exploit the monolingual data for self-training, in
which monolingual sentences with higher uncertainty would be sampled with
higher probability. Experimental results on large-scale WMT
English$\Rightarrow$German and English$\Rightarrow$Chinese datasets demonstrate
the effectiveness of the proposed approach. Extensive analyses suggest that
emphasizing the learning on uncertain monolingual sentences by our approach
does improve the translation quality of high-uncertainty sentences and also
benefits the prediction of low-frequency words at the target side.
