An Ample Approach to Data and Modeling (2110.01776v2)

Abstract: In the present work, we describe a framework for modeling how models can be built that integrates concepts and methods from a wide range of fields. The information schism between the real-world and that which can be gathered and considered by any individual information processing agent is characterized and discussed, followed by the presentation of a series of the adopted requisites while developing the modeling approach. The issue of mapping from datasets into models is subsequently addressed, as well as some of the respectively implied difficulties and limitations. Based on these considerations, an approach to meta modeling how models are built is then progressively developed. First, the reference M* meta model framework is presented, which relies critically in associating whole datasets and respective models in terms of a strict equivalence relation. Among the interesting features of this model are its ability to bridge the gap between data and modeling, as well as paving the way to an algebra of both data and models which can be employed to combine models into hierarchical manner. After illustrating the M* model in terms of patterns derived from regular lattices, the reported modeling approach continues by discussing how sampling issues, error and overlooked data can be addressed, leading to the $M^{<\epsilon>}$ variant, illustrated respectively to number theory. The situation in which the data needs to be represented in terms of respective probability densities is treated next, yielding the $M^{<\sigma>}$ meta model, which is then illustrated respectively to a real-world dataset (iris flowers data). Several considerations about how the developed framework can provide insights about data clustering, complexity, collaborative research, deep learning, and creativity are then presented, followed by overall conclusions.