In structural alignments of RNA sequences, the computational cost of Sankoff algorithm, which simultaneously optimizes the score of the common secondary structure and the score of the alignment, is too high for long sequences (O(L6) time for two sequences of length L). In this chapter, we introduce the methods that predict the structures and the alignment separately to avoid the heavy computations in Sankoff algorithm. In those methods, neither of those two prediction processes is independent, but each of them utilizes the information of the other process. The first process typically includes prediction of base-pairing probabilities (BPPs) or the candidates of the stems, and the alignment process utilizes those results. At the same time, it is also important to reflect the information of the alignment to the structure prediction. This idea can be implemented as the probabilistic transformation (PCT) of BPPs using the potential alignment. As same as for all the estimation problems, it is important to define the evaluation measure for the structural alignment. The principle of maximum expected accuracy (MEA) is applicable for sum-of-pairs (SPS) score based on the reference alignment.
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