Deterministic annealing EM algorithm
Neural Networks
Near optimal multiple alignment within a band in polynomial time
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
LSMS/ICSEE'10 Proceedings of the 2010 international conference on Life system modeling and simulation and intelligent computing, and 2010 international conference on Intelligent computing for sustainable energy and environment: Part III
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Objective:: Deterministic annealing, which is derived from statistical physics, is a method for obtaining the global optimum in parameter space. During the annealing process, starting from high temperatures which are then lowered, deterministic annealing deterministically find the (global) optimum at each temperature. Thus, deterministic annealing is expected to be more computationally efficient than stochastic sampling strategies to obtain the global optimum. We propose to apply the deterministic annealing technique to the problem of efficiently finding the biologically optimal alignment of multiple sequences. Methods and material:: We take a strategy based on probabilistic models for aligning multiple sequences. That is, we train a probabilistic model using given training sequences and obtain their alignment by parsing, i.e. searching for the most likely parse of each sequence and gaps using the trained parameters of the model. In this scenario, we propose a new stochastic model, which is simple enough to be suited to multiple sequence alignment and, unlike existing stochastic models, say a profile hidden Markov model (HMM), allows us to use similarity scores between symbols (or a symbol and a gap). We further present a learning algorithm for our simple model by combining deterministic annealing with an expectation-maximization (EM) algorithm. We emphasize that our approach is time-efficient, even if the training is done through an annealing process. Results:: In our experiments, we used actual protein sequences whose three-dimensional (3D) structures are determined and which are all aligned based on their 3D structures. We compared the results obtained by our approach with those by other existing approaches. Experimental results clearly showed that our approach gave the best performance, in terms of the similarity to the structurally determined alignment, among the approaches tested. Experimental results further indicated that our approach was ten times more efficient in terms of actual computation time than a competing method.