Density Estimation with Genetic Programming for Inverse Problem Solving
This paper addresses the resolution, by Genetic Programming (GP) methods, of ambiguous inverse problems, where for a single input, many outputs can be expected. We propose two approaches to tackle this kind of many-to-one inversion problems, each of them based on the estimation, by a team of predictors, of a probability density of the expected outputs. In the first one, Stochastic Realisation GP, the predictors outputs are considered as the realisations of an unknown random variable which distribution should approach the expected one. The second one, Mixture Density GP, directly models the expected distribution by the mean of a Gaussian mixture model, for which genetic programming has to find the parameters. Encouraging results are obtained on four test problems of different difficulty, exhibiting the interests of such methods.
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- 1.Bishop, C.M.: Mixture density networks. Technical report, Aston University (1994)Google Scholar
- 5.Platel, M.D., Chami, M., Clergue, M., Collard, P.: Teams of genetic predictors for inverse problem solving. In: Keijzer, M., Tettamanzi, A.G.B., Collet, P., van Hemert, J.I., Tomassini, M. (eds.) EuroGP 2005. LNCS, vol. 3447, pp. 341–350. Springer, Heidelberg (2005)Google Scholar
- 8.Morishita, R., Imade, H., Ono, I., Ono, N., Okamoto, M.: Finding multiple solutions based on an evolutionary algorithm for inference of genetic networks by s-system. In: Congress on Evolutionary Computation, CEC ’03, pp. 615–622 (2003)Google Scholar
- 10.Spector, L.: Autoconstructive evolution: Push, pushGP, and pushpop. In: Proceedings of the Genetic and Evolutionary Computation Conference, GECCO-2001, 7-11 July 2001, pp. 137–146. Morgan Kaufmann, San Francisco (2001)Google Scholar
- 11.Streichert, F., Planatscher, H., Spieth, C., Ulmer, H., Zell, A.: Comparing genetic programming and evolution strategies on inferring gene regulatory networks. In: Genetic and Evolutionary Computation – GECCO-2004, Part I, pp. 471–480, Seattle, WA, USA (2004)Google Scholar
- 13.Yao, X.: Universal approximation by genetic programming. In: Foundations of Genetic Programming, Orlando, Florida, USA, 13 (1999)Google Scholar