Abstract
The main theme is to show that a one-hidden-layer neural network, which has learned a Bayesian discriminant function, can be used for estimating hidden Markov chains. The crucial point of the algorithm is the use of the logistic function as the activation of the output unit of the network. The network learns a single discriminant function, but converts it to the individual discriminant functions at all the steps.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Duda, R.O., Hart, P.E.: Pattern classification and scene analysis. John Wiley & Sons, New York (1973)
Churchill, G.: Stochastic models for heterogeneous DNA sequences. Bull. Math. Biology 51(1), 79–94 (1989)
Funahashi, K.: Multilayer neural networks and Bayes decision theory. Neural Networks 11, 209–213 (1998)
Ito, Y.: Simultaneous approximations of polynomials and derivatives and their applications to neural networks. Neural Computation 20, 2757–2791 (2008)
Ito, Y., Srinivasan, C.: Multicategory Bayesian decision using a three-layer neural network. In: Kaynak, O., Alpaydın, E., Oja, E., Xu, L. (eds.) ICANN/ICONIP 2003. LNCS, vol. 2714, pp. 253–261. Springer, Heidelberg (2003)
Ito, Y., Srinivasan, C.: Bayesian decision theory on three-layer neural networks. Neurocomputing 63, 209–228 (2005)
Ito, Y., Srinivasan, C., Izumi, H.: Bayesian learning of neural networks adapted to changes of prior probabilities. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds.) ICANN 2005. LNCS, vol. 3697, pp. 253–259. Springer, Heidelberg (2005)
Ito, Y., Srinivasan, C., Izumi, H.: Discriminant analysis by a neural network with Mahalanobis distance. In: Kollias, S.D., Stafylopatis, A., Duch, W., Oja, E. (eds.) ICANN 2006, Part II. LNCS, vol. 4132, pp. 350–360. Springer, Heidelberg (2006)
Ito, Y., Srinivasan, C., Izumi, H.: Learning of Bayesian discriminant functions by a neural network. In: Ishikawa, M., Doya, K., Miyamoto, H., Yamakawa, T. (eds.) ICONIP 2007, Part I. LNCS, vol. 4984, pp. 238–247. Springer, Heidelberg (2008)
Ito, Y., Srinivasan, C., Izumi, H.: Multi-category Bayesian decision by neural networks. In: Kůrková, V., Neruda, R., KoutnÃk, J. (eds.) ICANN 2008, Part I. LNCS, vol. 5163, pp. 21–30. Springer, Heidelberg (2008)
Ito, Y., Izumi, H., Srinivasan, C.: Learning of Mahalanobis discriminant functions by a neural network. In: Leung, C.S., Lee, M., Chan, J.H. (eds.) ICONIP 2009, Part I. LNCS, vol. 5863, pp. 417–424. Springer, Heidelberg (2009)
Khasminskii, R., Lazareva, B., Stapleton, J.: Some procedures for state estimation of a hidden Markov chain with two states. In: Gupta, S.S., Berger, J. (eds.) Statistical Decision Theory and Related Topics, pp. 477–487. Springer (1994)
Ruck, D.W., Rogers, S.K., Kabrisky, M., Oxley, M.E., Suter, B.W.: The multilayer perceptron as an approximation to a Bayes optimal discriminant function. IEEE Transactions on Neural Networks 1, 296–298 (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Ito, Y., Izumi, H., Srinivasan, C. (2014). Estimation of Hidden Markov Chains by a Neural Network. In: Loo, C.K., Yap, K.S., Wong, K.W., Teoh, A., Huang, K. (eds) Neural Information Processing. ICONIP 2014. Lecture Notes in Computer Science, vol 8834. Springer, Cham. https://doi.org/10.1007/978-3-319-12637-1_75
Download citation
DOI: https://doi.org/10.1007/978-3-319-12637-1_75
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12636-4
Online ISBN: 978-3-319-12637-1
eBook Packages: Computer ScienceComputer Science (R0)