Abstract
In this chapter recent research in the area of multi-objective optimisation of regression models is presented and combined. Evolutionary multi-objective optimisation techniques are described for training a population of regression models to optimise the recently defined Regression Error Characteristic Curves (REC). A method which meaningfully compares across regressors and against benchmark models (i.e. ‘random walk’ and maximum a posteriori approaches) for varying error rates. Through bootstrapping training data, degrees of confident out-performance are also highlighted.
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J.S. Armstrong and F. Collopy. Error measures for generalizing about forecasting methods: Empirical comparisons. International Journal of Forecasting, 8(1):69–80, 1992.
J. Bi and K.P. Bennett. Regression Error Characteristic Curves. In Proceedings of the Twentieth International Conference on Machine Learning (ICML-2003), pages 43–50, Washington DC, 2003.
C.M. Bishop. Neural Networks for Pattern Recognition. Oxford University Press, 1998.
C.A. Coello Coello. A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques. Knowledge and Information Systems. An International Journal, 1(3):269–308, 1999.
I. Das and J. Dennis. A closer look at drawbacks of minimizing weighted sums of objectives for pareto set generation in multicriteria optimization problems. Structural Optimization, 14(1):63–69, 1997.
K. Deb. Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, Chichester, 2001.
K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan. Fast and elitist multiobjective genetic algorithm: NSGA–II,. IEEE Transactions on Evolutionary Computation, 6(2):182–197, 2002.
B. Efron and R.J. Tibshirani. An Introduction to the Bootstrap. Number 57 in Monographs on Statistics and Probability. Chapman & Hall, New York, 1993.
R.M. Everson, J.E. Fieldsend, and S. Singh. Full Elite Sets for Multi-Objective Optimisation. In I.C. Parmee, editor, Adaptive Computing in Design and Manufacture V, pages 343–354. Springer, 2002.
J.E. Fieldsend and R.M. Everson. ROC Optimisation of Safety Related Systems. In J. Hernández-Orallo, C. Ferri, N. Lachiche, and P. Flach, editors, Proceedings of ROCAI 2004, part of the 16th European Conference on Artificial Intelligence (ECAI), pages 37–44, Valencia, Spain, 2004.
J.E. Fieldsend and R.M. Everson. Multi-objective Optimisation in the Presence of Uncertainty. In Proceedings of the IEEE Congress on Evolutionary Computation (CEC’05), 2005. Forthcoming.
J.E. Fieldsend, R.M. Everson, and S. Singh. Using Unconstrained Elite Archives for Multi-Objective Optimisation. IEEE Transactions on Evolutionary Computation, 7(3):305–323, 2003.
J.E. Fieldsend, J. Matatko, and M. Peng. Cardinality constrained portfolio optimisation. In Z.R. Yang, R. Everson, and H. Yin, editors, Proceedings of the Fifth International Conference on Intelligent Data Engineering and Automated Learning (IDEAL’04), number 3177 in Lecture Notes in Computer Science, pages 788–793. Springer, 2004.
J.E. Fieldsend and S. Singh. A Multi-Objective Algorithm based upon Particle Swarm Optimisation, an Efficient Data Structure and Turbulence. In Proceedings of UK Workshop on Computational Intelligence (UKCI’02), pages 37–44, Birmingham, UK, Sept. 2–4, 2002.
J.E. Fieldsend and S. Singh. Pareto Multi-Objective Non-Linear Regression Modelling to Aid CAPM Analogous Forecasting. In Proceedings of the 2002 IEEE International Joint Conference on Neural Networks, pages 388–393, Hawaii, May 12–17, 2002. IEEE Press.
J.E. Fieldsend and S. Singh. Optimizing forecast model complexity using multiobjective evolutionary algorithms. In C.A.C Coello and G.B. Lamont, editors, Applications of Multi-Objective Evolutionary Algorithms, pages 675–700. World Scientific, 2005.
C.M. Fonseca and P.J. Fleming. An Overview of Evolutionary Algorithms in Multiobjective Optimization. Evolutionary Computation, 3(1):1–16, 1995.
M.T. Jensen. Reducing the run-time complexity of multiobjective EAs: The NSGA–II and other algorithms. IEEE Transactions on Evolutionary Computation, 7(5):503–515, 2003.
Y. Jin, T. Okabe, and B. Sendhoff. Neural network regularization and ensembling using multi-objective evolutionary algorithms. In Proceedings of the IEEE Congress on Evolutionary Computation (CEC’04), pages 1–8. IEEE Press, 2004.
J. Knowles and D. Corne. The pareto archived evolution strategy: A new baseline algorithm for pareto multiobjective optimisation. In Proceedings of the 1999 Congress on Evolutionary Computation, pages 98–105, Piscataway, NJ, 1999. IEEE Service Center.
J.D. Knowles and D. Corne. Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy. Evolutionary Computation, 8(2):149–172, 2000.
M. Laumanns, L. Thiele, and E. Zitzler. Running Time Analysis of Multiobjective Evolutionary Algorithms on Pseudo-Boolean Functions. IEEE Transactions on Evolutionary Computation, 8(2):170–182, 2004.
M. Laumanns, L. Thiele, E. Zitzler, E. Welzl, and K. Deb. Running Time Analysis of Multi-objective Evolutionary Algorithms on a Simple Discrete Optimization Problem. In J.J. Merelo Guervós, P. Adamidis, H-G Beyer, J-L Fernández-Villacañas, and H-P Schwefel, editors, Parallel Problem Solving from Nature—PPSN VII, Lecture Notes in Computer Science, pages 44–53. Springer- Verlag, 2002 2002.
Y. LeCun, J. Denker, S. Solla, R. E. Howard, and L. D. Jackel. Optimal brain damage. In D. S. Touretzky, editor, Advances in Neural Information Processing Systems II, pages 598–605, San Mateo, CA, 1990. Morgan Kauffman.
Y. Liu and X. Yao. Towards designing neural network ensembles by evolution. Lecture Notes in Computer Science, 1498:623–632, 1998.
S. Mostaghim, J. Teich, and A. Tyagi. Comparison of Data Structures for Storing Pareto-sets in MOEAs. In Congess on Evolutionary Computation (CEC’2002), volume 1, pages 843–848, Piscataway, New Jersey, May 2002. IEEE Press.
I.T. Nabney. Netlab: Algorithms for Pattern Recognition. Springer, 2002.
Y. Raviv and N. Intrator. Bootstrapping with noise: An effective regularization technique. Connection Science, 8:356–372, 1996.
K.I. Smith, R.M. Everson, and J.E. Fieldsend. Dominance Measures for Multi- Objective Simulated Annealing. In Proceedings of the IEEE Congress on Evolutionary Computation (CEC’04), pages 23–30. IEEE Press, 2004.
J. Utans and J. Moody. Selecting neural network architectures via the prediction risk: application to corporate bond rating prediction. In Proc. of the First Int. Conf on AI Applications on Wall Street, pages 35–41, Los Alamos, CA, 1991. IEEE Computer Society Press.
D. Van Veldhuizen and G. Lamont. Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art. Evolutionary Computation, 8(2):125–147, 2000.
A. S. Weigend and N. A. Gershenfeld, editors. Time Series Prediction: Forecasting the Future and Understanding the Past. Addison-Wesley, Reading, MA, 1994.
D. Wolpert. On bias plus variance. Neural Computation, 9(6):1211–1243, 1997.
X. Yao. Evolving Artificial Neural Networks. Proceedings of the IEEE, 87(9):1423–1447, 1999.
E. Zitzler. Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications. PhD thesis, Swiss Federal Institute of Technology Zurich (ETH), 1999. Diss ETH No. 13398.
E. Zitzler and L. Thiele. Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Transactions on Evolutionary Computation, 3(4):257–271, 1999.
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Fieldsend, J.E. (2006). Regression Error Characteristic Optimisation of Non-Linear Models. In: Jin, Y. (eds) Multi-Objective Machine Learning. Studies in Computational Intelligence, vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33019-4_5
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DOI: https://doi.org/10.1007/3-540-33019-4_5
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