Abstract

We consider Conditional Random Fields (CRFs) with pattern-based potentials defined on a chain. In this model the energy of a string (labeling) x1 . . . xn is the sum of terms over intervals [i, j] where each term is nonzero only if the substring xi . . . xj 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(nL), O(nL`max ) and O(nL min{|D|, log(`max+1)}) where L is the combined length of input patterns, `max is the maximum length of a pattern, and D is the input alphabet. This improves on the previous algorithms of (Ye et al., 2009) whose complexities
are respectively O(nL|D|), and O(nL|D|), where 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.