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Conclusion

In this section, the leaving-one-out  technique and the different smoothing techniques have been applied to the estimation of probabilities in stochastic language modelling   only. However, it should be stressed that the techniques presented are by no means limited to language modelling. They may be useful in similar areas, where probabilistic models are applied and the number of free parameters to be trained  is large. Examples of such fields are probabilistic grammars , machine learning, machine translation, information retrieval and database queries, probabilistic reasoning in expert systems, and any other field in which information is processed, decisions are taken and the sparseness   of training data  must be explicitly taken into account. For noiseless  source coding, see the textbook by Bell, Cleary and Witten [Bell et al. (1990), p. 144,].   



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