# Inference algorithms for pattern-based CRFs on sequence data

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Rustem Takhanov,
Vladimir Kolmogorov
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Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):145-153, 2013.

#### Abstract

We consider \em Conditional Random Fields (CRFs) with pattern-based potentials defined on a chain. In this model the energy of a string (labeling) x_1\ldots x_n is the sum of terms over intervals [i,j] where each term is non-zero only if the substring x_i\ldots x_j equals a prespecified pattern α. Such CRFs can be naturally applied to many sequence tagging problems. We present efficient algorithms for the three standard inference tasks in a CRF, namely computing (i) the partition function, (ii) marginals, and (iii) computing the MAP. Their complexities are respectively O(n L), O(n L \ell_\max) and O(n L \min{|D|,\log (\ell_\max + 1)}) where L is the combined length of input patterns, \ell_\max is the maximum length of a pattern, and D is the input alphabet. This improves on the previous algorithms of \citeYe:NIPS09 whose complexities are respectively O(n L |D|), O\left(n |Γ| L^2 \ell_\max^2\right) and O(n L |D|), where |Γ| is the number of input patterns. In addition, we give an efficient algorithm for sampling, and revisit the case of MAP with non-positive weights. Finally, we apply pattern-based CRFs to the problem of the protein dihedral angles prediction.

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