System models or learning machines?

摘要

This paper focuses on the issues and challenges that are encountered in the area of modeling, identification and state estimation of environmental and economic systems. It is argued that the traditional modeling and identification approach is not appropriate for the highly complex systems that we deal with nowadays in environmental science and economics. We propose that the researchers shift their attention and efforts from attempting to actually develop system models to designing algorithms that get the machine to learn about the behavior of the system. We attempt to make the case that traditional modeling techniques do not work for complex systems by introducing the notion of ‘hard’ and ‘soft’ variables. The advantages of machine learning theory and how it can be used to assess the quality of a given model (or learning machine) are discussed. A new approach that implements the notion of VC dimension and the principle of structural risk minimization is proposed to link system macro-descriptions to agent-based models. The techniques of support vector machines and kernel learning are discussed, and explanations as to how kernels can reproduce the knowledge expressed in (empirical and universal) laws are provided. Finally, a small application to the problem of spatial downscaling of the GDP aggregate data is presented.