%0 Conference Paper %1 eurogp07:defoin %A Defoin Platel, Michael %A Verel, Sébastien %A Clergue, Manuel %A Chami, Malik %B Proceedings of the 10th European Conference on Genetic Programming %C Valencia, Spain %D 2007 %E Ebner, Marc %E O'Neill, Michael %E Ekárt, Anikó %E Vanneschi, Leonardo %E Esparcia-Alcázar, Anna Isabel %I Springer %K algorithms, genetic programming %P 45--54 %R doi:10.1007/978-3-540-71605-1_5 %T Density estimation with Genetic Programming for Inverse Problem solving %V 4445 %X 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. %@ 3-540-71602-5

@inproceedings{eurogp07:defoin, abstract = {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.}, added-at = {2008-06-19T17:35:00.000+0200}, address = {Valencia, Spain}, author = {{Defoin Platel}, Michael and Verel, S\'ebastien and Clergue, Manuel and Chami, Malik}, biburl = {https://www.bibsonomy.org/bibtex/267800ed62e8af87703158d7701816f80/brazovayeye}, booktitle = {Proceedings of the 10th European Conference on Genetic Programming}, doi = {doi:10.1007/978-3-540-71605-1_5}, editor = {Ebner, Marc and O'Neill, Michael and Ek\'art, Anik\'o and Vanneschi, Leonardo and Esparcia-Alc\'azar, Anna Isabel}, interhash = {06c2f873bb6df47052f576c1c3582b4d}, intrahash = {67800ed62e8af87703158d7701816f80}, isbn = {3-540-71602-5}, isbn13 = {978-3-540-71602-0}, keywords = {algorithms, genetic programming}, month = {11 - 13 April}, notes = {Part of \cite{ebner:2007:GP} EuroGP'2007 held in conjunction with EvoCOP2007, EvoBIO2007 and EvoWorkshops2007}, pages = {45--54}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, timestamp = {2008-06-19T17:38:32.000+0200}, title = {Density estimation with Genetic Programming for Inverse Problem solving}, volume = 4445, year = 2007 }