Abstract
A common language modeling approach assumes the data D is generated from a mixture of several language models. EM algorithm is usually used to find the maximum likelihood estimation of one unknown mixture component, given the mixture weights and the other language models. In this paper, we provide an efficient algorithm of O(k) complexity to find the exact solution, where k is the number of words occurred at least once in D. Another merit is that the probabilities of many words are exactly zeros, which means that the mixture language model also serves as a feature selection technique.
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