Abstract
Hidden Markov Models (HMMs) have been successfully used in tasks involving prediction and recognition of patterns in sequence data, with applications in areas such as speech recognition and bioinformatics. While variations of traditional HMMs proved to be practical in applications where it is feasible to obtain the numerical probabilities required for the specification of the parameters of the model and the probabilities available are descriptive of the underlying uncertainty, the capabilities of HMMs remain unexplored in applications where this convenience is not available. Motivated by such applications, we present a HMM that uses qualitative probabilities instead of quantitative ones. More specifically, the HMM presented here captures the order of magnitude of the probabilities involved instead of numerical probability values. We analyze the resulting model by using it to perform classification tasks on gene expression data.
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References
A. Darwiche and M. Goldszmidt. On the relation between kappa calculus and probabilistic reasoning. In Proceedings of the Tenth Annual Conference on Uncertainty in Artificial Intelligence (UAI), pages 145–153, 1994.
P. D’haeseleer, S. Liang, and R. Somogyi. Gene expression data analysis and modeling. Tutorial, University of New Mexico, 1999.
M. Fox, M. Ghallab, G. Infantes, and D. Long. Robot introspection through learned Hidden Markov Models. Artificial Intelligence, 170(2):59–113, 2006.
N. Friedman. Inferring cellular networks using probabilistic graphical Models. Science, 303:799–805, 2004.
M. Goldszmidt and J. Pearl. Qualitative probabilities for default reasoning, belief revision, and causal modeling. Artifi Intell., 84(1–2):57–112, 1996.
D. Hand. Protection or privacy? data mining and personal data. In Proceedings of the 10th Pacific-Asia Conference, Advances in Knowledge Discovery and Data Mining (PAKDD), pages 1–10, 2006.
X. Huang, A. Acero, and H.W. Hon. Spoken Language Processing: A Guide to Theory, Algorithm and System Development. Prentice Hall PTR, 2001.
A. Ibrahim, A. Tawfik, and A. Ngom. A qualitative Hidden Markov Model for spatio-temporal reasoning. In Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, (ECSQARU), pages 707–718, 2007.
A. Jepson and R. Mann. Qualitative probabilities for image interpretation. In Proceedings of the International Conference on Computer Vision-Volume 2 (ICCV), pages 1123–1130, 1999.
R. Kahsay, G. Gao, and L. Liao. An improved Hidden Markov Model for transmembrane protein detection and topology prediction and its applications to complete genomes. Bioinformatics, 21(9):853–1858, 2005.
H. Kyburg. Probabiliity and the logic of rational belief. Technical report, Wesleyan Universit Press, 1961.
B. Lovell. Hidden Markov Models for spatio-temporal pattern recognition and image segmentation, 2001.
Z. Lubovac, B. Olsson, P. Jonsson, K. Laurio, and M.L. Andersson. Biological and statistical evaluation of gene expression profiles. In Proceedings of Mathematics and Computers in Biology and Chemistry, pages 149–155, 2001.
S. Parsons. Hybrid models of uncertainty in protein topology prediction. Applied Artificial Intelligence, 9(3):335–351, 1995.
S. Parsons. Qualitative probability and order of magnitude reasoning. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 11(3):373–390, 2003.
Rabiner. A tutorial on Hidden Markov Models and selected applications in speech recognition. Proceedings of the IEEE, 77(2):257–289, 1989.
V. Ramezani and S. Marcus. Estimation of Hidden Markov Models: risk-sensitive filter banks and qualitative analysis of their sample paths. IEEE Transactios on Automatic Control, 47(12): 1000–2009, 2002.
A. Rosti and M. Gales. Factor analysed Hidden Markov Models for speech recognition. Technical Report 453, Cambridge University Engineering Department, 2003.
A. Schliep, A. Schonhuth, and C. Steinhoff. Using Hidden Markov Models to analyse gene expression time course data. Bioinformatics, 19(1):1255–1263, 2003.
P Smyth. Belief Networks, Hidden Markov Models, and Markov Random Fields: A unifying view. Pattern Recognition Letters, 18(11–13): 1261–1268, 1997.
W. Spohn. Ordinal conditional functions: A dynamic theory of epistemic states. Causation in Decision, Belief Change, and Statistics, 2:105–134, 1987.
M. Wellman. Some varieties of qualitative probability. In Proceedings of th e5th International Conference on Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU), pages 171–179, 1994.
Y. Zeng and J. Garcia-Frias. A novel HMM-based clustering algorithm for the analysis of gene expression time-course data. Computational Statistics & Data Analysis, 50:2472–2494, 2006.
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Ibrahim, Z.M., Tawfik, A.Y., Ngom, A. (2009). Qualitative Hidden Markov Models for Classifying Gene Expression Data. In: Bramer, M., Petridis, M., Coenen, F. (eds) Research and Development in Intelligent Systems XXV. SGAI 2008. Springer, London. https://doi.org/10.1007/978-1-84882-171-2_4
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DOI: https://doi.org/10.1007/978-1-84882-171-2_4
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