Bigram

A bigram or digram is a sequence of two adjacent elements from a string of tokens, which are typically letters, syllables, or words. A bigram is an n-gram for n=2. The frequency distribution of every bigram in a string is commonly used for simple statistical analysis of text in many applications, including in computational linguistics, cryptography, speech recognition, and so on.

Gappy bigrams or skipping bigrams are word pairs which allow gaps (perhaps avoiding connecting words, or allowing some simulation of dependencies, as in a dependency grammar).

Head word bigrams are gappy bigrams with an explicit dependency relationship.

Bigrams help provide the conditional probability of a token given the preceding token, when the relation of the conditional probability is applied:

${\displaystyle P(W_{n}|W_{n-1})={P(W_{n-1},W_{n}) \over P(W_{n-1})}}$

That is, the probability ${\displaystyle P()}$ of a token ${\displaystyle W_{n}}$ given the preceding token ${\displaystyle W_{n-1}}$ is equal to the probability of their bigram, or the co-occurrence of the two tokens ${\displaystyle P(W_{n-1},W_{n})}$, divided by the probability of the preceding token.

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