How to process uncertainty in machine learning?

Uncertainty is a popular phenomenon in machine learning and a variety of methods to model uncertainty at different levels has been developed. The aim of this paper is to motivate the merits and problems when dealing with uncertainty in machine learning and to give an overview about methodologies which fall under the framework of neurofuzzy methods, in particular fuzzy-clustering on the one side and fuzzy inference systems on the other side. 1 Areas dealing with uncertainty Uncertainty and fuzziness are popular phenomena in many application areas such as medicine (medical diagnosis is often not crisp but there exist various degrees of illness e.g. for psychical diseases such as phobia), image processing (areas at object borders or at overlapping regions can seldom uniquely be classified), linguistics (terms such as ‘high’ or ‘small’ are context dependent), etc. Therefore, uncertainty almost automatically occurs in any application of machine learning. Different types of uncertainty can be observed: (i) Input data are subject to noise, outliers, and errors. A machine learning method has to deal with this type of fuzzy information, showing robustness with respect to such disturbances. Thereby, input noise can have a positive effect on the generalization behavior of the machine learning method since the method is forced to develop some form of invariance and to abstract from the noise. (ii) Output decisions should be accompanied by a measure which allows to judge the certainty or belief of the output. This is particularly important in critical domains such as clinical diagnosis, in safety critical areas, or in semiautomatic systems where human expert knowledge is accompanied by automatic inference. (iii) Representation of information within a machine learning system is distributed and fuzzy. This is the standard situation for classical neural network models and it is difficult to assign a crisp meaning to specific parts of a neural model. For a deeper insight into the network behavior, an interpretation of the fuzzy information in the internal representation is required. According to these different locations and goals of fuzzy information, a variety of different models exist which allow machine learning to deal with insecure information as input, output, or internal representation. 79 ESANN'2007 proceedings European Symposium on Artificial Neural Networks Bruges (Belgium), 25-27 April 2007, d-side publi., ISBN 2-930307-07-2.