Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider Conditional random fields (CRFs) with pattern-based potentials defined on a chain. In this model the energy of a string (labeling) $$x_1\ldots x_n$$x1źxn is the sum of terms over intervals [i, j] where each term is non-zero only if the substring $$x_i\ldots x_j$$xiźxj equals a prespecified pattern w. Such CRFs can be naturally applied to many sequence tagging problems.  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 $$O(\textit{nL})$$O(nL), $$O(\textit{nL} \ell _{\max })$$O(nLlmax) and $$O(\textit{nL} \min \{|D|,\log (\ell _{\max }\!+\!1)\})$$O(nLmin{|D|,log(lmax+1)}) where L is the combined length of input patterns, $$\ell _{\max }$$lmax 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 $$O(\textit{nL} |D|)$$O(nL|D|), $$O\left( n |\varGamma | L^2 \ell _{\max }^2\right) $$On|Γ|L2lmax2 and $$O(\textit{nL} |D|)$$O(nL|D|), where $$|\varGamma |$$|Γ| is the number of input patterns. In addition,  give an efficient algorithm for sampling, and revisit the case of MAP with non-positive ights.
['Rustem Takhanov', 'Vladimir Kolmogorov']
I am writing a research paper on a idea Inference algorithms for pattern-based CRFs on sequence data
[{"from": "human", "value": "I am writing a research paper on a idea Inference algorithms for pattern-based CRFs on sequence data"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider Conditional random fields (CRFs) with pattern-based potentials defined on a chain. In this model the energy of a string (labeling) $$x_1\\ldots x_n$$x1\u017axn is the sum of terms over intervals [i, j] where each term is non-zero only if the substring $$x_i\\ldots x_j$$xi\u017axj equals a prespecified pattern w. Such CRFs can be naturally applied to many sequence tagging problems.  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 $$O(\\textit{nL})$$O(nL), $$O(\\textit{nL} \\ell _{\\max })$$O(nLlmax) and $$O(\\textit{nL} \\min \\{|D|,\\log (\\ell _{\\max }\\!+\\!1)\\})$$O(nLmin{|D|,log(lmax+1)}) where L is the combined length of input patterns, $$\\ell _{\\max }$$lmax 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 $$O(\\textit{nL} |D|)$$O(nL|D|), $$O\\left( n |\\varGamma | L^2 \\ell _{\\max }^2\\right) $$On|\u0393|L2lmax2 and $$O(\\textit{nL} |D|)$$O(nL|D|), where $$|\\varGamma |$$|\u0393| is the number of input patterns. In addition,  give an efficient algorithm for sampling, and revisit the case of MAP with non-positive ights."}]