Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
 All Pages
mars


Multivariate Adaptive Regression Spline (MARS)

Specification

Alias: none

Argument(s): none

Required/Optional Description of Group Dakota Keyword Dakota Keyword Description
Optional max_bases

Maximum number of MARS bases

Optional interpolation

MARS model interpolation type

Optional export_model

Exports surrogate model in user-selected format

Description

This surface fitting method uses multivariate adaptive regression splines from the MARS3.5 package[26] developed at Stanford University.

The MARS reference material does not indicate the minimum number of data points that are needed to create a MARS surface model. However, in practice it has been found that at least $n_{c_{quad}}$, and sometimes as many as 2 to 4 times $n_{c_{quad}}$, data points are needed to keep the MARS software from terminating. Provided that sufficient data samples can be obtained, MARS surface models can be useful in SBO and OUU applications, as well as in the prediction of global trends throughout the parameter space.

Theory

The form of the MARS model is based on the following expression:

\[ \hat{f}(\mathbf{x})=\sum_{m=1}^{M}a_{m}B_{m}(\mathbf{x}) \]

where the $a_{m}$ are the coefficients of the truncated power basis functions $B_{m}$, and $M$ is the number of basis functions. The MARS software partitions the parameter space into subregions, and then applies forward and backward regression methods to create a local surface model in each subregion. The result is that each subregion contains its own basis functions and coefficients, and the subregions are joined together to produce a smooth, $C^{2}$-continuous surface model.

MARS is a nonparametric surface fitting method and can represent complex multimodal data trends. The regression component of MARS generates a surface model that is not guaranteed to pass through all of the response data values. Thus, like the quadratic polynomial model, it provides some smoothing of the data.