The performance of neural machine translation systems is commonly evaluated in terms of BLEU. However, due to its reliance on target language properties and generation, the BLEU metric does not allow an assessment of which translation directions are more difficult to model. In this paper, we propose cross-mutual information (XMI): an asymmetric information-theoretic metric of machine translation difficulty that exploits the probabilistic nature of most neural machine translation models. XMI allows us to better evaluate the difficulty of translating text into the target language while controlling for the difficulty of the target-side generation component independent of the translation task. We then present the first systematic and controlled study of cross-lingual translation difficulties using modern neural translation systems. Code for replicating our experiments is available online at https://github.com/e-bug/nmt-difficulty.
Topic models are a useful analysis tool to uncover the underlying themes within document collections. Probabilistic models which assume a generative story have been the dominant approach for topic modeling. We propose an alternative approach based on clustering readily available pre-trained word embeddings while incorporating document information for weighted clustering and reranking top words. We provide benchmarks for the combination of different word embeddings and clustering algorithms, and analyse their performance under dimensionality reduction with PCA. The best performing combination for our approach is comparable to classical models, and complexity analysis indicate that this is a practical alternative to traditional topic modeling.