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Energy-Based Models (EBMs) allow for extremely flexible specifications of probability distributions. However, they do not provide a mechanism for obtaining exact samples from these distributions. Monte Carlo techniques can aid us in obtaining samples if some proposal distribution that we can easily sample from is available. For instance, rejection sampling can provide exact samples but is often difficult or impossible to apply due to the need to find a proposal distribution that upper-bounds the target distribution everywhere. Approximate Markov chain Monte Carlo sampling techniques like Metropolis-Hastings are usually easier to design, exploiting a local proposal distribution that performs local edits on an evolving sample. However, these techniques can be inefficient due to the local nature of the proposal distribution and do not provide an estimate of the quality of their samples. In this work, we propose a new approximate sampling technique, Quasi Rejection Sampling (QRS), that allows for a trade-off between sampling efficiency and sampling quality, while providing explicit convergence bounds and diagnostics. QRS capitalizes on the availability of high-quality global proposal distributions obtained from deep learning models. We demonstrate the effectiveness of QRS sampling for discrete EBMs over text for the tasks of controlled text generation with distributional constraints and paraphrase generation. We show that we can sample from such EBMs with arbitrary precision at the cost of sampling efficiency.

@article{eikema-et-al-2021-sampling,
  author    = {Bryan Eikema and
               Germ{\'{a}}n Kruszewski and
               Hady Elsahar and
               Marc Dymetman},
  title     = {Sampling from Discrete Energy-Based Models with Quality/Efficiency
               Trade-offs},
  journal   = {CoRR},
  volume    = {abs/2112.05702},
  year      = {2021},
  url       = {https://arxiv.org/abs/2112.05702},
  eprinttype = {arXiv},
  eprint    = {2112.05702}
}

In neural machine translation (NMT), we search for the mode of the model distribution to form predictions. The mode as well as other high probability translations found by beam search have been shown to often be inadequate in a number of ways. This prevents practitioners from improving translation quality through better search, as these idiosyncratic translations end up being selected by the decoding algorithm, a problem known as the beam search curse. Recently, a sampling-based approximation to minimum Bayes risk (MBR) decoding has been proposed as an alternative decision rule for NMT that would likely not suffer from the same problems. We analyse this approximation and establish that it has no equivalent to the beam search curse, i.e. better search always leads to better translations. We also design different approximations aimed at decoupling the cost of exploration from the cost of robust estimation of expected utility. This allows for exploration of much larger hypothesis spaces, which we show to be beneficial. We also show that it can be beneficial to make use of strategies like beam search and nucleus sampling to construct hypothesis spaces efficiently. We show on three language pairs (English into and from German, Romanian, and Nepali) that MBR can improve upon beam search with moderate computation.

@article{eikema-aziz-2021-sampling,
  author    = {Bryan Eikema and
               Wilker Aziz},
  title     = {Sampling-Based Minimum Bayes Risk Decoding for Neural Machine Translation},
  journal   = {CoRR},
  volume    = {abs/2108.04718},
  year      = {2021},
  url       = {https://arxiv.org/abs/2108.04718},
  eprinttype = {arXiv},
  eprint    = {2108.04718}
}

Recent studies have revealed a number of pathologies of neural machine translation (NMT) systems. Hypotheses explaining these mostly suggest there is something fundamentally wrong with NMT as a model or its training algorithm, maximum likelihood estimation (MLE). Most of this evidence was gathered using maximum a posteriori (MAP) decoding, a decision rule aimed at identifying the highest-scoring translation, i.e. the mode. We argue that the evidence corroborates the inadequacy of MAP decoding more than casts doubt on the model and its training algorithm. In this work, we show that translation distributions do reproduce various statistics of the data well, but that beam search strays from such statistics. We show that some of the known pathologies and biases of NMT are due to MAP decoding and not to NMT's statistical assumptions nor MLE. In particular, we show that the most likely translations under the model accumulate so little probability mass that the mode can be considered essentially arbitrary. We therefore advocate for the use of decision rules that take into account the translation distribution holistically. We show that an approximation to minimum Bayes risk decoding gives competitive results confirming that NMT models do capture important aspects of translation well in expectation.

@inproceedings{eikema-aziz-2020-is,
    title = "Is MAP Decoding All You Need? The Inadequacy of the Mode in Neural Machine Translation",
    author = "Eikema, Bryan  and
      Aziz, Wilker",
    booktitle = "Proceedings of the 28th International Conference on Computational Linguistics",
    month = dec,
    year = "2020",
    address = "Barcelona, Spain",
    publisher = "Association for Computational Linguistics",
}