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this NLP book gives

When we use a bigram model to predict the conditional probability of the next word, we are thus making the following approximation:

$P(w_n|w_1^{n-1}) \approx P(w_n|w_{n-1})$

does $w_1^{n-1}$ denote whole the sentence?

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On page 3, the notation is defined:

We'll represent a sequence of $N$ words either as $w_1 \ldots w_n$ or $w_1^n$ (so the expression $w_1^{n-1}$ means the string $w_1, w_2, \ldots, w_{n−1}$).

So yes, it represents the sequence of words from $w_1$ to $w_{n-1}$, i.e. the whole sentence up to that point.

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  • $\begingroup$ However, in the special case where the sequence $w_i$ is a Markov chain, then knowing $w_{n-1}$ is the same as knowing $w_1^{n-1}.$ $\endgroup$ – BruceET Jul 26 '19 at 3:48
  • $\begingroup$ Thanks for you answer. $w_1^n$. Here has nothing to do with exponential computation, right? $\endgroup$ – czlsws Jul 27 '19 at 22:49
  • $\begingroup$ Nothing at all, they're just using the superscript to differentiate the two symbols. $\endgroup$ – ConMan Jul 29 '19 at 0:45

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