Conditional random field

Conditional random fields (CRFs) are a class of statistical modeling method often applied in pattern recognition and machine learning and used for structured prediction. CRFs fall into the sequence modeling family. Whereas a discrete classifier predicts a label for a single sample without considering 'neighboring' samples, a CRF can take context into account; e.g., the linear chain CRF (which is popular in natural language processing) predicts sequences of labels for sequences of input samples.Let G = ( V , E ) {displaystyle G=(V,E)} be a graph such that Conditional random fields (CRFs) are a class of statistical modeling method often applied in pattern recognition and machine learning and used for structured prediction. CRFs fall into the sequence modeling family. Whereas a discrete classifier predicts a label for a single sample without considering 'neighboring' samples, a CRF can take context into account; e.g., the linear chain CRF (which is popular in natural language processing) predicts sequences of labels for sequences of input samples. CRFs are a type of discriminative undirected probabilistic graphical model. They are used to encode known relationships between observations and construct consistent interpretations and are often used for labeling or parsing of sequential data, such as natural language processing or biological sequencesand in computer vision.Specifically, CRFs find applications in POS tagging, shallow parsing,named entity recognition,gene finding and peptide critical functional region finding,among other tasks, being an alternative to the related hidden Markov models (HMMs). In computer vision, CRFs are often used for object recognition and image segmentation. Lafferty, McCallum and Pereira define a CRF on observations X {displaystyle {oldsymbol {X}}} and random variables Y {displaystyle {oldsymbol {Y}}} as follows: What this means is that a CRF is an undirected graphical model whose nodes can be divided into exactly two disjoint sets X {displaystyle {oldsymbol {X}}} and Y {displaystyle {oldsymbol {Y}}} , the observed and output variables, respectively; the conditional distribution p ( Y | X ) {displaystyle p({oldsymbol {Y}}|{oldsymbol {X}})} is then modeled. For general graphs, the problem of exact inference in CRFs is intractable. The inference problem for a CRF is basically the same as for an MRF and the same arguments hold.However, there exist special cases for which exact inference is feasible: