jurafsky&martin_3rdEd_17 (1).pdf

Wed like a metric that shares our intuition that

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the surface error. We’d like a metric that shares our intuition that giraffe is a more likely source than grail for graffe because giraffe is closer in spelling to graffe than grail is to graffe . The minimum edit distance algorithm from Chapter 2 will play a role here. But we’d also like to prefer corrections that are more frequent words, or more likely to occur in the context of the error. The noisy channel model introduced in the next section offers a way to formalize this intuition. Real word spelling error detection is a much more difficult task, since any word in the input text could be an error. Still, it is possible to use the noisy channel to find candidates for each word w typed by the user, and rank the correction that is most likely to have been the users original intention. 5.1 The Noisy Channel Model In this section we introduce the noisy channel model and show how to apply it to the task of detecting and correcting spelling errors. The noisy channel model was applied to the spelling correction task at about the same time by researchers at AT&T Bell Laboratories ( Kernighan et al. 1990 , Church and Gale 1991 ) and IBM Watson Research (Mays et al., 1991) . decoder noisy word original word noisy channel guessed word noisy 1 noisy 2 noisy N word hyp1 word hyp2 ... word hyp3 Figure 5.1 In the noisy channel model, we imagine that the surface form we see is actually a “distorted” form of an original word passed through a noisy channel. The decoder passes each hypothesis through a model of this channel and picks the word that best matches the surface noisy word. The intuition of the noisy channel model (see Fig. 5.1 ) is to treat the misspelled noisy channel word as if a correctly spelled word had been “distorted” by being passed through a noisy communication channel. This channel introduces “noise” in the form of substitutions or other changes to the letters, making it hard to recognize the “true” word. Our goal, then, is to build a model of the channel. Given this model, we then find the true word by passing every word of the language through our model of the noisy channel and seeing which one comes the closest to the misspelled word.
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5.1 T HE N OISY C HANNEL M ODEL 63 This noisy channel model is a kind of Bayesian inference . We see an obser- Bayesian vation x (a misspelled word) and our job is to find the word w that generated this misspelled word. Out of all possible words in the vocabulary V we want to find the word w such that P ( w | x ) is highest. We use the hat notation ˆ to mean “our estimate of the correct word”. ˆ w = argmax w 2 V P ( w | x ) (5.1) The function argmax x f ( x ) means “the x such that f ( x ) is maximized”. Equa- argmax tion 5.1 thus means, that out of all words in the vocabulary, we want the particular word that maximizes the right-hand side P ( w | x ) .
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