Epi-Splines: Tools for Data Analysis and Function Identification


Johannes O. Royset
Associate Professor
Operations Research Department
Naval Postgraduate School, Monterey, CA


Wednesday, October 30
4:15 - 5:15 PM


Abstract:

Demanding engineering, business, and statistical applications require data analysis in contexts with little data, too much data, missing data, multi-source data, and subjective data. In particular, the fusion of observations with external information derived from experiences and established ``laws'' results in challenging problems that go much beyond standard procedures. We present a broad framework for identifying a function that according to some criterion best represents a given data set and satisfies constraints derived from the data as well as external information. These function identification problems lead to constrained infinite-dimensional optimization that includes as special cases most of the classical fitting, estimation, and regression problems. The framework allows any constraints, for example related to shape restrictions, enables studies of information growth such as from a larger sample, and facilitates the usually unavoidable approximations needed to make a procedure computationally tractable. The central components of the framework are epi-splines: the piecewise polynomial functions that are structurally related to standard splines, but are more flexible and arise more broadly. The framework is used in uncertainty quantification, probability density estimation, financial curve and variogram construction, commodity price and electricity demand forecasting, and simulation output analysis. The presentation gives an overview of the framework and discusses applications.

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Operations Research Colloquia: http://or.stanford.edu/oras_seminars.html