From Numeric to Granular Models: A Quest for Error and Performance Analysis.

Abstract

In this study, we establish a new design methodology of granular models realized by augmenting the existing numeric models through analyzing and modeling their associated prediction error. Several novel approaches to the construction of granular architectures through augmenting existing numeric models by incorporating modeling errors are proposed in order to improve and quantify the numeric models' prediction abilities. The resulting construct arises as a granular model that produces granular outcomes generated as a result of the aggregation of the outputs produced by the numeric model (or its granular counterpart) and the corresponding error terms. Three different architectural developments are formulated and analyzed. In comparison with the numeric models, which strive to achieve the highest accuracy, granular models are developed in a way such that they produce comprehensive prediction outcomes realized as information granules. In virtue of the granular nature of results, the coverage and specificity of the constructed information granules express the quality of the results of prediction in a more descriptive and comprehensive manner. The performance of the granular constructs is evaluated using the criteria of coverage and specificity, which are pertinent to granular outputs produced by the granular models.