Imprecise Regression Based on Possibilistic Likelihood

Abstract

Machine learning, and more specifically regression, usually focuses on the search for a precise model, when precise data are available. It is well-known that the model thus found may not exactly describe the target concept, due to the existence of learning biases. So, we are interested in a learning process that accounts also for the uncertainty around the predicted value which should not be illusionary precise. The goal of imprecise regression is to find a model that offers a good trade-off between faithfulness w.r.t. data and (meaningful) precision. The function that is learnt associates, to each input vector, a possibility distribution which represents a family of probability distributions. Based on this interpretation of a possibilistic distribution, we define the notion of possibilistic likelihood. Then, we propose a framework of imprecise regression based on the previous notion and a particle swarm optimization process. This approach takes advantage of the capability of triangular possibility distributions to approximate any unimodal probability distribution from above. We illustrate our approach with a generated dataset.