Back-translation has become a commonly employed heuristic for semi-supervised neural machine translation. The technique is both straightforward to apply and has led to state-of-the-art results. In this work, we offer a principled interpretation of back-translation as approximate inference in a generative model of bitext and show how the standard implementation of back-translation corresponds to a single iteration of the wake-sleep algorithm in our proposed model. Moreover, this interpretation suggests a natural iterative generalization, which we demonstrate leads to further improvement of up to 1.6 BLEU.
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