# Complexity of constraint satisfaction

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In computer science, the **inside–outside algorithm** is a way of re-estimating production probabilities in a probabilistic context-free grammar. It was introduced James K. Baker in 1979 as a generalization of the forward–backward algorithm for parameter estimation on hidden Markov models to stochastic context-free grammars. It is used to compute expectations, for example as part of the expectation–maximization algorithm (an unsupervised learning algorithm).

## Inside and outside probabilities

The inside probability is the total probability of generating words , given the root nonterminal and a grammar :^{[1]}

The outside probability is the total probability of beginning with the start symbol and generating the nonterminal and all the words outside , given a grammar :^{[1]}

## References

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- J. Baker (1979): Trainable grammars for speech recognition. In J. J. Wolf and D. H. Klatt, editors,
*Speech communication papers presented at the 97th meeting of the Acoustical Society of America*, pages 547–550, Cambridge, MA, June 1979. MIT. - Karim Lari, Steve J. Young (1990): The estimation of stochastic context-free grammars using the inside–outside algorithm.
*Computer Speech and Language*, 4:35–56. - Karim Lari, Steve J. Young (1991): Applications of stochastic context-free grammars using the Inside–Outside algorithm.
*Computer Speech and Language*, 5:237–257. - Fernando Pereira, Yves Schabes (1992): Inside–outside reestimation from partially bracketed corpora.
*Proceedings of the 30th annual meeting on Association for Computational Linguistics, Association for Computational Linguistics*, 128–135.

## External links

- An implementation of the algorithm by Mark Johnson
- Inside-outside algorithm - Fei Xia
- The Inside-Outside Algorithm - Michael Collins

- ↑
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