a. [10 pts] Write down the formula for Dirichlet Prior Smoothing. Then, mathematically prove the following...

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a. [10 pts] Write down the formula for Dirichlet Prior Smoothing. Then, mathematically prove the following two lemmas: O Show, in the limit where document length tends to infinity, that a unigram language model smoothed with a Dirichlet prior becomes equivalent to one estimated using the maximum likelihood estimate. Show, in the limit where the parameter µ tends to infinity, that a unigram language model smoothed with a Dirichlet prior becomes equivalent to the background language model used in the smoothing. b. [5 pts] Point out one advantage of Jelinek-Mercer smoothing over Katz-Backoff smoothing. Explain why. a. [10 pts] Write down the formula for Dirichlet Prior Smoothing. Then, mathematically prove the following two lemmas: O Show, in the limit where document length tends to infinity, that a unigram language model smoothed with a Dirichlet prior becomes equivalent to one estimated using the maximum likelihood estimate. Show, in the limit where the parameter µ tends to infinity, that a unigram language model smoothed with a Dirichlet prior becomes equivalent to the background language model used in the smoothing. b. [5 pts] Point out one advantage of Jelinek-Mercer smoothing over Katz-Backoff smoothing. Explain why.

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Dirichlet Prior Smoothing is a method used in language modeling to address the sparsity problem enco... View the full answer