In the seminal paper “Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data“, Lafferty, McCallum, Pereira (2001) introduce a very popular type of Markov random field for segmentation. Conditional Random Fields (CRFs) are used in many fields including machine translation, parsing, genetics, and transmission codes.  They are a non-directed version of Hidden Markov Networks.  The paper describes conditional random fields, provides an iterative method to estimate the parameters of the CRF, and reports experimental comparisons between CRFs, hidden Markov models, and maximum entropy Markov models.

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