Evaluating Neural Spatial Interaction Modelling by Bootstrapping

Fischer, Manfred M. and Reismann, Martin (2000): Evaluating Neural Spatial Interaction Modelling by Bootstrapping. Published in: Networks and Spatial Economics , Vol. 2, No. 3 (2002): pp. 255-268.

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 = 9] 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Neural spatial interaction modelling, model evaluation, bootstrapping, interregional telecommunications
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C21 - Cross-Sectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C45 - Neural Networks and Related Topics

References

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

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

Efron B, Tibshirani R (1991) Statistical data analysis in the computer age. Science 253: 390-394

Efron B, Tibshirani R (1993) An introduction to the bootstrap. Chapman and Hall, New York

Fischer M M, Gopal S (1994) Artificial neural networks: A new approach to modelling interregional telecommunciation flows. Journal of Regional Science 34(4): 503-527

Fischer M M, Hlavackova-Schindler K, Reismann M (1999) A global search procedure for parameter estimation in neural spatial interaction modelling. Papers in Regional Science 78: 119-134

Fischer, M M (1998) Computational neural networks: A new paradigm for spatial analysis. Environment and Planning A 30 (10): 1873-1891

Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Networks 2: 359-366

LeBaron B, Weigend A S (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, Duval R D (1993) Bootstrapping: A nonparametric approach to statistical inference. Sage Publications, Newbury Park (CA)

Openshaw S (1993) Modelling spatial interaction using a neural net. In Fischer MM, Nijkamp P (eds) Geographical information systems, spatial modelling, and policy evaluation, pp. 147-164. Springer, Berlin

Openshaw S (1998) Neural network, genetic, and fuzzy logic models of spatial interaction. Environment and Planning A 30: 1857-1872

Storn R, Price K (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, Huberman B A, Rumelhart D E (1990) Predicting the future: A connectionist approach. International Journal of Neural Systems 1: 193-209