Inference algorithms for pattern-based CRFs on sequence data

We consider Conditional Random Fields (CRFs) with pattern-based potentials defined on a chain. In this model the energy of a string (labeling) x ₁... x_n is the sum of terms over intervals [i, j] where each term is non-zero only if the substring x_i... 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), 0(nLℓ_max) and O(nL min{|D|, log(ℓ_max+1)}) where L is the combined length of input patterns, ℓ_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\), O (n|Γ|L²ℓ_max²) and O(nL\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.