Paper available: Visualization of High-Dimensional Functions

[charles@playfair.Stanford.EDU]

The following doctoral dissertation (168 pages) is now available 
electronically: 

	ftp://playfair.stanford.edu/pub/roosen/thesis.ps.Z


A short (6 page) proceedings paper on the same material is also available:

	ftp://playfair.stanford.edu/pub/roosen/asa95.ps.Z




Charles Roosen				charles at playfair.stanford.edu
Department of Statistics		http://playfair.stanford.edu/~roosen/
Stanford University

Title
-----

Visualization and Exploration of High-Dimensional Functions 
Using the Functional ANOVA Decomposition


Abstract
--------

In recent years the statistical and engineering communities have
developed many high-dimensional methods for regression (e.g.\ MARS,
feedforward neural networks, projection pursuit).  Users of these
methods often wish to explore how particular predictors affect the
response.  One way to do so is by decomposing the model into low-order
components through a functional ANOVA decomposition and then
visualizing the components.  Such a decomposition, with the
corresponding variance decomposition, also provides information on the
importance of each predictor to the model, the importance of
interactions, and the degree to which the model may be represented by
first and second-order components.

This manuscript develops techniques for constructing and exploring such
a decomposition.  It begins by suggesting techniques for constructing the
decomposition either numerically or analytically, proceeds to describe 
approaches to plotting and interpreting effects, and then develops
methodology for rough inference and model selection.  Extensions to the
GLM framework are discussed briefly.