Making regression imprecise for providing a better representation of precise data
Résumé
Machine learning, and more specifically regression, usually focus on the search for a precise model, when precise data are available. Moreover, it is well-known that the model thus found may not exactly describe the target concept, due to the existence of learning bias. In order to overcome the problem of learning too much illusionary precise models, a so-called imprecise regression from non-fuzzy input and output data has been proposed recently by the authors mainly on an empirical basis. The goal of imprecise regression is to find a model that has the better tradeoff between faithfulness w.r.t. data and (meaningful) precision. Imprecise regression uses an optimization algorithm that produces linear or non-linear (kernel-based) fuzzy regression functions. These functions associate to a precise input vector a possibility distribution that is likely to restrict the output value. In this paper, we proposed a modified version of the initial approach, try to relate it to the representation of family of probabilities by means of possibility distributions. This approach is compared with classical and fuzzy regression frameworks. Experiments on an environmental database are performed and the interest of fuzzy predictions.