@article{1794,
abstract = {We consider Conditional random fields (CRFs) with pattern-based potentials defined on a chain. In this model the energy of a string (labeling) (Formula presented.) is the sum of terms over intervals [i, j] where each term is non-zero only if the substring (Formula presented.) equals a prespecified pattern w. 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 (Formula presented.), (Formula presented.) and (Formula presented.) where L is the combined length of input patterns, (Formula presented.) is the maximum length of a pattern, and D is the input alphabet. This improves on the previous algorithms of Ye et al. (NIPS, 2009) whose complexities are respectively (Formula presented.), (Formula presented.) and (Formula presented.), where (Formula presented.) 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.},
author = {Kolmogorov, Vladimir and Takhanov, Rustem},
journal = {Algorithmica},
number = {1},
pages = {17 -- 46},
publisher = {Springer},
title = {{Inference algorithms for pattern-based CRFs on sequence data}},
doi = {10.1007/s00453-015-0017-7},
volume = {76},
year = {2016},
}
@inproceedings{2272,
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 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 & 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. },
author = {Takhanov, Rustem and Kolmogorov, Vladimir},
booktitle = {ICML'13 Proceedings of the 30th International Conference on International},
location = {Atlanta, GA, USA},
number = {3},
pages = {145 -- 153},
publisher = {International Machine Learning Society},
title = {{Inference algorithms for pattern-based CRFs on sequence data}},
volume = {28},
year = {2013},
}