An Ample Approach to Data and Modeling
  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.
