Hierarchy-Based Partition Models: Using Classification Hierarchies to Improve the Statistical Estimation of Bigrams

We propose a novel machine learning technique that can be used to estimate probability distributions for categorical random variables that are equipped with a natural set of classification hierarchies, such as words equipped with word class hierarchies, wordnet hierarchies, and suffix and affix hierarchies. We evaluate the estimator on bigram language modelling with a hierarchy based on word suffixes, using English, Danish, and Finnish data from the Europarl corpus with training sets of up to 1–1.5 million words. The results show that the proposed estimator outperforms modified Kneser-Ney smoothing in terms of perplexity on unseen data. This suggests that important information is hidden in the classification hierarchies that we routinely use in computational linguistics, but that we are unable to utilize this information fully because our current statistical techniques are either based on simple counting models or designed for sample spaces with a distance metric, rather than sample spaces with a non-metric topology given by a classification hierarchy. Keywords: machine learning; categorical variables; classification hierarchies; language modelling; statistical estimation