DataModeler—A New Kind of Modeling

Letting the Data Speak for Itself

Mark Kotanchek

Evolved Analytics, LLC

Abstract

Conventional data modeling typically follows one of three paths: (1) assume a first-principles model and determine the coefficients which best fit the data; (2) assume a mathematically tractable model form (e.g., low-order polynomial) and fit that to the data; or (3) assume a flexible nonlinear model structure (e.g., neural network, support vector machine, etc.) and fit that to the data in a black-box fashion taking care that the nonlinear model isn't too nonlinear. A key to success in each of these is that the supplied input variables are both significant and independent. Unfortunately, in the real world we often are presented with highly multivariate data with unknown relationships between the inputs as well as the targeted response.

An alternative—which is implemented in the soon-to-be-released DataModeler add-on package for Mathematica—is to allow flexibility in structure and variable combinations and let survival-of-the-fittest guide the development of models which are accurate, robust and simple. This approach is surprisingly efficient and leads to white-box models which can be insightful as the selected variables, variable combinations and model forms are examined. Furthermore, ensembles of diverse high-quality models can be used to create trustable models which are able to detect operation in new operating regions or fundamental system changes.

In this talk, we will illustrate DataModeler's ability to handle a variety of data set types (small, large, fat, skinny, ill-conditioned, etc.) as well some of the real-world success stories (industrial, research, ecological and social science data modeling, design optimization, etc.). Along the way we will also demonstrate the infrastructure supporting the overall modeling process from data import and exploration through model development, deployment and maintenance.