jurafsky&martin_3rdEd_17 (1).pdf

The computations in fig 55 show that our

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The computations in Fig. 5.5 show that our implementation of the noisy channel model chooses across as the best correction, and actress as the second most likely word. Unfortunately, the algorithm was wrong here; the writer’s intention becomes clear from the context: . . . was called a “stellar and versatile acress whose com- bination of sass and glamour has defined her. . . ”. The surrounding words make it clear that actress and not across was the intended word.
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5.2 R EAL - WORD SPELLING ERRORS 67 For this reason, it is important to use larger language models than unigrams. For example, if we use the Corpus of Contemporary American English to compute bigram probabilities for the words actress and across in their context using add-one smoothing, we get the following probabilities: P(actress | versatile) = . 000021 P(across | versatile) = . 000021 P(whose | actress) = . 0010 P(whose | across) = . 000006 Multiplying these out gives us the language model estimate for the two candi- dates in context: P(“versatile actress whose”) = . 000021 . 0010 = 210 10 - 10 P(“versatile across whose”) = . 000021 . 000006 = 1 10 - 10 Combining the language model with the error model in Fig. 5.5 , the bigram noisy channel model now chooses the correct word actress . Evaluating spell correction algorithms is generally done by holding out a train- ing, development and test set from lists of errors like those on the Norvig and Mitton sites mentioned above. 5.2 Real-word spelling errors The noisy channel approach can also be applied to detect and correct real-word spelling errors , errors that result in an actual word of English. This can happen from real-word error detection typographical errors (insertion, deletion, transposition) that accidentally produce a real word (e.g., there for three ) or because the writer substituted the wrong spelling of a homophone or near-homophone (e.g., dessert for desert , or piece for peace ). A number of studies suggest that between 25% and 40% of spelling errors are valid English words as in the following examples (Kukich, 1992) : This used to belong to thew queen. They are leaving in about fifteen minuets to go to her house. The design an construction of the system will take more than a year. Can they lave him my messages? The study was conducted mainly be John Black. The noisy channel can deal with real-word errors as well. Let’s begin with a version of the noisy channel model first proposed by Mays et al. (1991) to deal with these real-word spelling errors. Their algorithm takes the input sentence X = { x 1 , x 2 ,..., x k ,..., x n } , generates a large set of candidate correction sentences C ( X ) , then picks the sentence with the highest language model probability. To generate the candidate correction sentences, we start by generating a set of candidate words for each input word x i . The candidates, C ( x i ) , include every English word with a small edit distance from x i . With edit distance 1, a common choice (Mays et al., 1991) , the candidate set for the real word error thew (a rare word meaning ‘muscular strength’) might be C(thew) = { the, thaw, threw, them, thwe } .
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