Conditional random field

Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured prediction. Whereas a classifier predicts a label for a single sample without considering "neighbouring" samples, a CRF can take context into account. To do so, the predictions are modelled as a graphical model, which represents the presence of dependencies between the predictions. What kind of graph is used depends on the application. For example, in natural language processing, "linear chain" CRFs are popular, for which each prediction is dependent only on its immediate neighbours. In image processing, the graph typically connects locations to nearby and/or similar locations to enforce that they receive similar predictions. Other examples where CRFs are used are: labeling or parsing of sequential data for natural language processing or biological sequences, part-of-speech tagging, shallow parsing, named entity recognition, gene finding, peptide critical functional region finding, and object recognition and in computer vision. CRFs are a type of discriminative undirected probabilistic graphical model. Lafferty, McCallum and Pereira define a CRF on observations and random variables as follows: Let be a graph such that , so that is indexed by the vertices of . Then is a conditional random field when each random variable , conditioned on , obeys the Markov property with respect to the graph; that is, its probability is dependent only on its neighbours in G: where means that and are neighbors in . What this means is that a CRF is an undirected graphical model whose nodes can be divided into exactly two disjoint sets and , the observed and output variables, respectively; the conditional distribution 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.