Information geometry of adaptive systems

IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium, AS-SPCC 2000

Volumn , Issue , 2000, Pages 12-17

  Amari, S ^a   Ozeki, T ^a   Park, H ^a,b  

^a RIKEN BRAIN SCIENCE INSTITUTE   (Japan)

^b Yonsei University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE CONTROL SYSTEMS; DYNAMICS; FISHER INFORMATION MATRIX; GEOMETRY; MULTILAYERS; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; SIGNAL PROCESSING; STOCHASTIC SYSTEMS; TOPOLOGY;

CONDITIONAL PROBABILITY DENSITY; FISHER INFORMATION METRIC; GEOMETRICAL STRUCTURE; INFORMATION GEOMETRY; MODEL SELECTION CRITERIA; NATURAL GRADIENT LEARNING; STOCHASTIC ENVIRONMENT; TOPOLOGICAL STRUCTURE;

HIERARCHICAL SYSTEMS;

EID: 84962426097     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ASSPCC.2000.882438     Document Type: Conference Paper

References (15)

1. Amari S., "Theory of Adaptive Pattern Classifiers", IEEE Trans., EC-16, No. 3, pp. 299-307, 1967.
2. Amari S., "Differential-geometrical method in statistics", Berlin: Springer, 1985.
3. Amari S., "Natural Gradient Works Efficiently in Learning", Neural Computation, 10, pp. 251-276, 1998.
4. Amari S., Cichocki A. and Yang H.H., "A New Learning Algorithm for Blind Signal Separation", Advances in Neural Information Processing Systems 8, Proceedings of the 1995 Conference NIPS, edited by David S. Touretzky, Michael C. Mozer and Michael E. Hasselmo, pp.757-763.
5. Amari S., Kurata K. and Nagaoka H., "Information Geometry of Boltzmann Machines", IEEE Trans. on Neural Networks, Vol. 3, No. 2, pp. 260-271, 1992.
6. Amari S. and Nagaoka H., "Information geometry", New York: AMS and Oxford University press, 2000.
7. Amari S., Park H. and Fukumizu K., "Adaptive method of realizing natural gradient learning for multilayer perceptrons", Submitted to Neural Computation 1999.
8. Chen A.M., Lu H. and Hecht-Nielsen R., "On the geometry of feedforward neural network error surfaces", Neural Computations, 5:910-927, 1993.
9. Kůrkova V. and Kainen P.C., "Functionally equivalent feedforward neural networks", Neural Computation, 6:543-558, 1994.
10. Park H., Amari S. and Fukumizu K., "Adaptive natural gradient learning algorithms for various stochastic models", Submitted 2000.
11. Rattray M., Saad D. and Amari S., "Natural Gradient Descent for On-Line Learning", Physical Review Letters, Vol. 81, No. 24, pp. 5461-5464, 1998.
12. Rüger S.M., and Ossen A., "The metric of weight space", Neural Processing Letters, 5:63-72, 1997.
13. Sussmann H.J., "Uniqueness of the weights for minimal feedforward nets with a given input-output map", Neural Networks, 5:589-593, 1992.
14. Yang H.H. and Amari S., "Complexity Issues in Natural Gradient Descent Method for Training Multilayer Perceptrons", Neural Computation, 10, pp. 2137-2157, 1998.
15. Watanabe S., "Algebraic analysis for non-identifiable learning machines", Neural Computation, to appear.