Observable operator models for discrete stochastic time series

Neural Computation

Volumn 12, Issue 6, 2000, Pages 1371-1398

  Jaeger, Herbert ^a  

^a FRAUNHOFER INSTITUTE FOR APPLIED INFORMATION TECHNOLOGY FIT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ARTIFICIAL NEURAL NETWORK; PROBABILITY; STATISTICAL MODEL; STATISTICS; TIME;

LINEAR MODELS; MARKOV CHAINS; NEURAL NETWORKS (COMPUTER); STOCHASTIC PROCESSES; TIME;

EID: 0034198996     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/089976600300015411     Document Type: Article

References (17)

1. Bengio, Y. (1996). Markovian models for sequential data (Tech. Rep. No. 1049). Montreal: Department d'Informatique et Recherche Opérationelle, Université de Montréal. Available online at: http://www.iro.umontreal.ca/labs/neuro/ pointeurs /hmmsTR.ps.
2. Berman, A., & Plemmons, R. (1979). Nonnegative matrices in the mathematical sciences. San Diego, CA: Academic Press.
3. Doob, J. (1953). Stochastic processes. New York: Wiley.
4. Elliott, R., Aggoun, L., & Moore, J. (1995). Hidden Markov models: Estimation and control. New York: Springer-Verlag.
5. Gilbert, E. (1959). On the identifiability problem for functions of finite Markov chains. Annals of Mathematical Statistics, 30, 688-697.
6. Golub, G., & Loan, C. van. (1996). Matrix computations (3rd ed.). Baltimore: Johns Hopkins University Press.
7. Heller, A. (1965). On stochastic processes derived from Markov chains. Annals of Mathematical Statistics, 36, 1286-1291.
8. Iosifescu, M., & Theodorescu, R. (1969). Random processes and learning. New York: Springer-Verlag.
9. Ito, H. (1992). An algebraic study of discrete stochastic systems. Unpublished doctoral dissertation, University of Tokyo, Bunkyo-ku, Tokyo, 1992. Available by ftp from http://kuro.is.sci.toho-u.ac.jp:8080/english/D/.
10. Ito, H., Amari, S.-I., & Kobayashi, K. (1992). Identifiability of hidden Markov information sources and their minimum degrees of freedom. IEEE Transactions on Information Theory, 38(2), 324-333.
11. Jaeger, H. (1997a). Observable operator models and conditioned continuation representations (Arbeitspapiere der GMD No. 1043). Sankt Augustin: GMD. A76ailable online at: http://www.gmd.de/People/Herbert.Jaeger/Publications.html.
12. Jaeger, H. (1997b). Observable operator models II: Interpretable models and model induction (Arbeitspapiere der GMD No. 1083). Sankt Augustin: GMD. Available online at: http://www.gmd.de/People/Herbert.Jaeger/Publications.html.
13. Jaeger, H. (1998). Discrete-time, discrete-valued observable operator models: A tutorial (GMD Report No. 42). Sankt Augustin: GMD. Available online at: http://www.gmd.de/People/Herbert.Jaeger/Publications.html.
14. Jaeger, H. (1999). Characterizing distributions of stochastic processes by linear operators (GMD report No. 62). Sankt Augustin: GMD. Available online at http://www.gmd.de/People/Herbert.Jaeger/Publications.html.
15. Narendra, K. (1995). Identification and control. In M. Arbib (Ed.), The handbook of brain theory and neural networks (pp. 477-480). Cambridge, MA: MIT Press/Bradford Books.
16. Rabiner, L. (1990). A tutorial on hidden Markov models and selected applications in speech recognition. In A. Waibel and K.-F. Lee (Eds.), Readings in speech recognition (pp. 267-296). San Mateo, CA: Morgan Kaufmann.
17. Smallwood, R., & Sondik, E. (1973). The optimal control of partially observable Markov processes over a finite horizon. Operations Research, 21, 1071-1088.