Genetic Programming with Boosting for Ambiguities in Regression Problems

Density Estimation with Genetic Programming for Inverse Problem Solving

“…One of the difficulty in comparing with published work is that, for the two alternatives presented here, the fitness function used is a φ-divergence, very useful for computing distance between two distributions but unusual in GP. As far as we know, the only previous GP work addressing explicitly the redundancy problem [9], is much more appropriated for functions decomposition, as the problem P a , than for more complex IP. Our SR-GP system can also easily solve P a , while MD-GP is much more suitable to tackle IP where complex densities have to be estimated.…”

“…In the GP field, several studies are related to IP solving (see for example [4,3,11,5]) but very few of them have investigated the question of the redundancy. However a noticeable exception can be found in [9] and will be discussed further. To overcome the non-uniqueness of the solution, instead of predicting the conditional mean, one way is to ensure that the output of an inverse model is at least one of the expected solutions [6].…”

“…Thus, one single GP program is responsible of producing multiple outputs. In [9], a technique based on boosting, that usually creates a posteriori mixtures of potential solutions, was extended to handle the ambiguity problem. Similarly, with the Parisian approach, used also to tackle an IP in [4], a subset of the population is selected to build the final answer.…”