Crf models encompass hidden markov band 20 2005 47

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Unformatted text preview: or modelling this type of data is called conditional random field (CRF, cf. Lafferty et al. (2001)). Again we consider the observed vector of words t and the corresponding vector of labels L. The labels have a graph structure. For a label Lc let N (c) be the indices of neighboring labels. Then (t, L) is a conditional random field when conditioned on the vector t of all terms the random variables obey the Markov property p( Lc |t, Ld ; d = c) = p( Lc |t, Ld ; d ∈ N (c)) (19) i.e. the whole vector t of observed terms and the labels of neighbors may influence the distribution of the label Lc . Note that we do not model the distribution p(t) of the observed words, which may exhibit arbitrary dependencies. We consider the simple case that the words t = (t1 , t2 , . . . , tn ) and the corresponding labels L1 , L2 , . . . , Ln have a chain structure and that Lc depends only on the preceding and succeeding labels Lc−1 and Lc+1 . Then the conditional distribution p(L|t) has the form ⎞ ⎛ n kj n −1 m j 1 p(L|t)...
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