Language modeling by variable length sequences: theoretical formulation and evaluation of multigrams

The multigram model assumes that language can be described as the output of a memoryless source that emits variable-length sequences of words. The estimation of the model parameters can be formulated as a Maximum Likelihood estimation problem from incomplete data. We show that estimates of the model parameters can be computed through an iterative Expectation-Maximization algorithm and we describe a forward-backward procedure for its implementation. We report the results of a systematical evaluation of multi-grams for language modeling on the ATIS database. The objective performance measure is the test set perplexity. Our results show that multigrams outperform conventional n-grams for this task.