Abstract
This paper exposes problems of the commonly used technique of splitting the available data in neural spatial interaction modelling into training, validation, and test sets that are held fixed and warns about drawing too strong conclusions from such static splits. Using a bootstrapping procedure, we compare the uncertainty in the solution stemming from the data splitting with model specific uncertainties such as parameter initialization. Utilizing the Austrian interregional telecommunication traffic data and the differential evolution method for solving the parameter estimation task for a fixed topology of the network model [i.e. J = 8] this paper illustrates that the variation due to different resamplings is significantly larger than the variation due to different parameter initializations. This result implies that it is important to not over-interpret a model, estimated on one specific static split of the data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Efron, B. (1982). The Jackknife, the Bootstrap and Other Resampling Plans. Philadelphia: Society for Industrial and Applied Mathematics.
Efron, B. and R. Tibshirani. (1993). An Introduction to the Bootstrap. New York: Chapman and Hall.
Fischer, M.M. (1998). “Computational Neural Networks: A New Paradigm for Spatial Analysis.” Environment and Planning A 30(10), 1873-1891.
Fischer, M.M. and S. Gopal. (1994). “Artificial Neural Networks: A New Approach to Modelling Interregional Telecommunication Flows.” Journal of Regional Science 34(4), 503-527.
Fischer, M.M., K. Hlavackova-Schindler, and M. Reismann. (1999). “A Global Search Procedure for Parameter Estimation in Neural Spatial Interaction Modelling.” Papers in Regional Science 78, 119-134.
Hornik, K., M. Stinchcombe, and H. White. (1989). “Multilayer Feedforward Networks are Universal Approximators.” Neural Networks 2, 359-366.
Kirkpatrick, S., C.D. Gelatt Jr., and M.P. Vecchi. (1983). “Optimization by Simulated Annealing.” Science 220, 671-680.
LeBaron, B. and A.S. Weigend. (1998). “A Bootstrap Evaluation of the Effect of Data Splitting on Financial Time Series.” IEEE Transactions on Neural Networks 9(1), 213-220.
Mooney, C.Z. and R.D. Duval. (1993). Bootstrapping: A Nonparametric Approach to Statistical Inference. Newbury Park, CA: Sage Publications.
Schwefel, H.-P. (1995). Evolution and Optimum Seeking. New York: Wiley.
Storn, R. and K. Price. (1997). “Differential Evolution-A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces.” Journal of Global Optimization 11, 341-359.
Tibshirani, R. (1996). “A Comparison of Some Error Estimates for Neural Network Models.” Neural Computation 8(1), 152-163.
Weigend, A.S., B.A. Huberman, and D.E. Rumelhart. (1990). “Predicting the Future: A Connectionist Approach.” International Journal of Neural Systems 1, 193-209.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fischer, M.M., Reismann, M. Evaluating Neural Spatial Interaction Modelling by Bootstrapping. Networks and Spatial Economics 2, 255–268 (2002). https://doi.org/10.1023/A:1019923727752
Issue Date:
DOI: https://doi.org/10.1023/A:1019923727752