Multinomial Loss on Held-out Data for the Sparse Non-negative Matrix Language Model

We describe Sparse Non-negative Matrix (SNM) language model estimation using multinomial loss on held-out data. Being able to train on held-out data is important in practical situations where the training data is usually mismatched from the held-out/test data. It is also less constrained than the previous training algorithm using leave-one-out on training data: it allows the use of richer meta-features in the adjustment model, e.g. the diversity counts used by Kneser-Ney smoothing which would be difficult to deal with correctly in leave-one-out training. In experiments on the one billion words language modeling benchmark, we are able to slightly improve on our previous results which use a different loss function, and employ leave-one-out training on a subset of the main training set. Surprisingly, an adjustment model with meta-features that discard all lexical information can perform as well as lexicalized meta-features. We find that fairly small amounts of held-out data (on the order of 30-70 thousand words) are sufficient for training the adjustment model. In a real-life scenario where the training data is a mix of data sources that are imbalanced in size, and of different degrees of relevance to the held-out and test data, taking into account the data source for a given skip-/n-gram feature and combining them for best performance on held-out/test data improves over skip-/n-gram SNM models trained on pooled data by about 8% in the SMT setup, or as much as 15% in the ASR/IME setup. The ability to mix various data sources based on how relevant they are to a mismatched held-out set is probably the most attractive feature of the new estimation method for SNM LM.