Learning in Neural Spatial Interaction Models: A Statistical Perspective

Fischer, Manfred M. (2002): Learning in Neural Spatial Interaction Models: A Statistical Perspective. Published in: Journal of Geographical Systems , Vol. 4, No. 3 (2002): pp. 287-299.

Abstract

In this paper we view learning as an unconstrained non-linear minimization problem in which the objective function is defined by the negative log-likelihood function and the search space by the parameter space of an origin constrained product unit neural spatial interaction model. We consider Alopex based global search, as opposed to local search based upon backpropagation of gradient descents, each in combination with the bootstrapping pairs approach to solve the maximum likelihood learning problem. Interregional telecommunication traffic flow data from Austria are used as test bed for comparing the performance of the two learning procedures. The study illustrates the superiority of Alopex based global search, measured in terms of Kullback and Leibler’s information criterion.

• Item Type: MPRA Paper
• Language: English
• Keywords: Maximum likelihood learning, local search, global search, backpropagation of gradient descents, Alopex procedure, origin constrained neural spatial interaction model
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C45 - Neural Networks and Related Topics

References

Bia, A. (2000): A study of possible improvements to the Alopex training algorithm, Proceedings of the VIth Brazilian Symposium on Neural Networks, pp. 125-130. IEEE Computer Society Press

Bishop, C.M. (1995): Neural networks for pattern recognition. Clarendon Press, Oxford.

Cichocki, A. and Unbehauen, R. (1993): Neural networks for optimization and signal processing. John Wiley, Chichester.

Efron, B. (1982): The jackknife, the bootstrap and other resampling plans. Society for Industrial and Applied Mathematics, Philadelphia

Fischer, M.M. and Reismann, M. (2002a): Evaluating neural spatial interaction modelling by bootstrapping, Networks and Spatial Economics [in press]

Fischer, M.M., and Reismann, M. (2002b): A methodology for neural spatial interaction modeling, Geographical Analysis 34(2) [in press]

Fischer, M.M., Reismann, M. and Hlavackova-Schindler, K. (2002): Neural network modelling of constrained spatial interaction flows: Design, estimation and performance issues, Journal of Regional Science 42 [in press]

Harth, E. and Pandya, A.S. (1988): Dynamics of ALOPEX process: Application to optimization problems. In Ricciardi, L.M. (ed.): Biomathematics and related computational problems, pp. 459-471. Kluwer, Dortrecht.

Hassoun, M.M. (1995): Fundamentals of neural networks. MIT Press, Cambridge and London.

Kirkpatrick, S., Gelatt, C.D. and Vecchi, M.P. (1983): Optimization by simulated annealing, Science 20, 671-680.

Kullback, S. and Leibler, R.A. (1951): On information and sufficiency, Annals of Mathematical Statistics 22, 78-86

Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1992): Numerical recipes in C: The art of scientific computing. Cambridge University Press, Cambridge

Rumelhart, D.E., Hinton, G.E. and Williams, R.J. (1986): Learning internal representations by error propagation. In Rumelhart, D.E., McClelland, J.L. and the PDP Research Group (eds.): Parallel distributed processing: Explorations in the microstructure of cognition, pp. 318-362. MIT Press, Cambridge [MA]

Rumelhart, D.E., Durbin, R., Golden, R. and Chauvin Y. (1995): Backpropagation: The basic theory. In Chauvin, Y. and Rumelhart, D.E. (eds.): Backpropagation: Theory, architectures and applications, pp. 1-34. Lawrence Erlbaum Associates, Hillsdale [NJ]

Unnikrishnan, K.P. and Venugopal, K.P. (1994): Alopex: A correlation-based learning algorithm for feedforward and recurrent neural networks, Neural Computation 6, 469-490