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There are two decoding algorithms essential to the area of natural language processing. One is the Viterbi algorithm for linear-chain models, such as HMMs or CRFs. The other is the CKY algorithm for probabilistic context free grammars. However, tasks such as noun phrase chunking and relation extraction seem to fall between the two, neither of them being the best fit. Ideally we would like to model entities and relations, with two layers of labels. We present a tractable algorithm for exact inference over two layers of labels and chunks with time complexity O(n2 ), and provide empirical results comparing. | Exact Decoding for Jointly Labeling and Chunking Sequences Nobuyuki Shimizu Department of Computer Science State University of New York at Albany Albany NY 12222 USA nobuyuki@shimi zu.name Andrew Haas Department of Computer Science State University of New York at Albany Albany NY 12222 USA haas@cs.albany.edu Abstract There are two decoding algorithms essential to the area of natural language processing. One is the Viterbi algorithm for linear-chain models such as HMMs or CRFs. The other is the CKY algorithm for probabilistic context free grammars. However tasks such as noun phrase chunking and relation extraction seem to fall between the two neither of them being the best fit. Ideally we would like to model entities and relations with two layers of labels. We present a tractable algorithm for exact inference over two layers of labels and chunks with time complexity O n2 and provide empirical results comparing our model with linear-chain models. 1 Introduction The Viterbi algorithm and the CKY algorithms are two decoding algorithms essential to the area of natural language processing. The former models a linear chain of labels such as part of speech tags and the latter models a parse tree. Both are used to extract the best prediction from the model Manning and Schutze 1999 . However some tasks seem to fall between the two having more than one layer but flatter than the trees created by parsers. For example in relation extraction we have entities in one layer and relations between entities as another layer. Another task is shallow parsing. We may want to model part-of-speech tags and noun verb chunks at the same time since performing simultaneous labeling may result in increased joint accuracy by sharing information between the two layers of labels. To apply the Viterbi decoder to such tasks we need two models one for each layer. We must feed the output of one layer to the next layer. In such an approach errors in earlier processing nearly always accumulate and .