Saul and Pereira, EMNLP 1997

Aggregate and mixed-order Markov modles for statistical language processing

This paper can be found at [1]

Citation

Lawrence Saul and Fernando Pereira. Aggregate and mixed-order Markov models for statistical language processing. In Proceedings of the Second Conference on Empirical Methods in Natural Language Processing, pages 81–89, Providence, Rhode Island, USA, August 1997.

Summary

The authors wanted to train a language model that used fewer parameters than an n-gram model, but still performed well. They developed aggregate and mixed-order markov models. While similar in some ways (mainly their Markovian properties), the new methods give fewer words 0 probability. It did perform worse than the n-gram models, but it used fewer parameters.

Aggregate Markov Models

They set $P(w_{2}|w_{1})=\sum _{i=1}^{C}P(w_{2}|c)P(c|w_{1})$ for some number of classes $C$.

Future Work

Aggregate Markov models can kinda be viewed as approximations of a full bigram model. In this way, the method is similar to SVD decomposition, which might be related. The classic question of generative vs discriminative models comes up. The authors argue that their generative model is fine because they train the mixture of generative models such that they model reality. Theirs models also train in a fraction of the time spent training Rosenfeld's models.

Related Work

• Rosenfeld, Computer Speech and Language 1996 worked on language models, but from a discriminative stance.
• Other combinations of language models include work done by Huang et al, Computer Speech and Language 1993 and Ney, et al, Computer Speech and Language 1994
• Jelinek et al, Advances in Speech Signal Processing 1992