Inference algorithms for pattern-based CRFs on sequence data JMLR Takhanov, Rustem Kolmogorov, Vladimir 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 non-zero 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(nLℓmax) and O(nLmin{|D|,log(ℓmax+1)}) where L is the combined length of input patterns, ℓmax 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|L2ℓ2max) and O(nL|D|), where |Γ| is the number of input patterns. In addition, we give an efficient algorithm for sampling. Finally, we consider the case of non-positive weights. (Komodakis &amp; Paragios, 2009) gave an O(nL) algorithm for computing the MAP. We present a modification that has the same worst-case complexity but can beat it in the best case. ML Research Press 2013 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text http://purl.org/coar/resource_type/c_5794 https://research-explorer.ista.ac.at/record/2272 Takhanov R, Kolmogorov V. Inference algorithms for pattern-based CRFs on sequence data. In: <i>ICML’13 Proceedings of the 30th International Conference on International</i>. Vol 28. ML Research Press; 2013:145-153. eng info:eu-repo/semantics/altIdentifier/wos/000381149500002 info:eu-repo/semantics/openAccess