text: IBM models are very important word alignment models in Machine Translation. Following the Maximum Likelihood Estimation principle to estimate their parameters, the models will easily overfit the training data when the data are sparse. While smoothing is a very popular solution in Language Model, there still lacks studies on smoothing for word alignment. In this paper, we propose a framework which generalizes the notable work Moore [2004] of applying additive smoothing to word alignment models. The framework allows developers to customize the smoothing amount for each pair of word. The added amount will be scaled appropriately by a common factor which reflects how much the framework trusts the adding strategy according to the performance on data. We also carefully examine various performance criteria and propose a smoothened version of the error count, which generally gives the best result.
  @cite_7: We investigate a number of simple methods for improving the word-alignment accuracy of IBM Model 1. We demonstrate reduction in alignment error rate of approximately 30 resulting from (1) giving extra weight to the probability of alignment to the null word, (2) smoothing probability estimates for rare words, and (3) using a simple heuristic estimation method to initialize, or replace, EM training of model parameters.
summary: However, there is still lack of studies for applying smoothing techniques to the word alignment problem. The work of this paper is mostly an extended work of @cite_7 which is the earliest study for this matter. In that work, Moore has an intensive study of many improvements to IBM Model 1. Additive smoothing is the first of the three improvements, which directly attempts to solve the sparsity problem. In spite of the simplicity, the method has good performance. The smoothing technique Moore applied is additive smoothing. For every pair of word @math , it is assumed that @math and @math were paired in a constant number of times before the training data is observed. Therefore, in each estimation, this assumption will be taken into account and the prior number of times, which they are paired, will be added appropriately. The constant prior count is tuned manually or learnt from some additional annotated data.