How to handle error bars in symbolic regression for data mining in scientific applications

Symbolic regression via genetic programming has become a very useful tool for the exploration of large databases for scientific purposes. The technique allows testing hundreds of thousands of mathematical models to find the most adequate to describe the phenomenon under study, given the data available. In this paper, a major refinement is described, which allows handling the problem of the error bars. In particular, it is shown how the use of the geodesic distance on Gaussian manifolds as fitness function allows taking into account the uncertainties in the data, from the beginning of the data analysis process. To exemplify the importance of this development, the proposed methodological improvement has been applied to a set of synthetic data and the results have been compared with more traditional solutions.