The goal of the workshop is a principled investigation of the coupling between what may be termed the "local information" having to do with a problem and more traditional questions about its global feasibility/complexity. Our quest is for radical new ways of reasoning about the local-to-global nature of information and computation, dealing with the internal structure of processes, whereby global truths are inferred from the substrate of local facts. One of our objective is to use ideas from mathematics, computer science, statistics, and information theory to formalize these disparate scenarios, and the tools used to understand them, into a common framework.

One example of this arises in social networks, where there is often substantial "small scale" structure, e.g., clusters in so-called ego networks, but where the global properties of the adjacency matrix or Laplacian matrix are more consistent with the hypothesis of unstructured noise. A second example of this arises with neural networks, where training overly-parameterized models against large quantities of data leads to localized structures in weight matrices that combine to achieve high quality (but brittle) models. A third example arises when considering fundamental questions of consistency of model classes. To enable handling rich probabilistic model classes in line with our expectations of what data must achieve, we must study a data-driven consistency framework, an innovation that also challenges the long-standing uniform/point-wise consistency dichotomy of statistical analysis. It shifts focus from the global complexity of the class to a form of local complexity that capture the local variation of properties within the model classes by means of topological formulations.

More generally, advances in computation and storage, combined with new technologies in areas from medicine to language processing, have produced a glut of data. With it comes a tremendous need for novel technologies and novel learning algorithms that translate raw data into knowledge. As is becoming increasingly clear, "big data has arrived but big insights have not" (T. Hartford, Financial Times). Turning data into insight hinges on our ability to frame problems on sound theoretical foundations, sometimes altering current methods fundamentally.