### Abstract

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|L^{2}ℓ_{max}
^{2}) 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.

Original language | English |
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Title of host publication | 30th International Conference on Machine Learning, ICML 2013 |

Publisher | International Machine Learning Society (IMLS) |

Pages | 1182-1190 |

Number of pages | 9 |

Edition | PART 2 |

Publication status | Published - 2013 |

Externally published | Yes |

Event | 30th International Conference on Machine Learning, ICML 2013 - Atlanta, GA, United States Duration: Jun 16 2013 → Jun 21 2013 |

### Other

Other | 30th International Conference on Machine Learning, ICML 2013 |
---|---|

Country | United States |

City | Atlanta, GA |

Period | 6/16/13 → 6/21/13 |

### Fingerprint

### ASJC Scopus subject areas

- Human-Computer Interaction
- Sociology and Political Science

### Cite this

*30th International Conference on Machine Learning, ICML 2013*(PART 2 ed., pp. 1182-1190). International Machine Learning Society (IMLS).

**Inference algorithms for pattern-based CRFs on sequence data.** / Takhanov, Rustem; Kolmogorov, Vladimir.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*30th International Conference on Machine Learning, ICML 2013.*PART 2 edn, International Machine Learning Society (IMLS), pp. 1182-1190, 30th International Conference on Machine Learning, ICML 2013, Atlanta, GA, United States, 6/16/13.

}

TY - GEN

T1 - Inference algorithms for pattern-based CRFs on sequence data

AU - Takhanov, Rustem

AU - Kolmogorov, Vladimir

PY - 2013

Y1 - 2013

N2 - 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... 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), 0(nLℓmax) and O(nL min{|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|L2ℓmax 2) 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.

AB - 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... 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), 0(nLℓmax) and O(nL min{|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|L2ℓmax 2) 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.

UR - http://www.scopus.com/inward/record.url?scp=84897534660&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84897534660&partnerID=8YFLogxK

M3 - Conference contribution

SP - 1182

EP - 1190

BT - 30th International Conference on Machine Learning, ICML 2013

PB - International Machine Learning Society (IMLS)

ER -