JSM 2005 Online Program

Abstract #304217

This is the preliminary program for the 2005 Joint Statistical Meetings in Minneapolis, Minnesota. Currently included in this program is the "technical" program, schedule of invited, topic contributed, regular contributed and poster sessions; Continuing Education courses (August 7-10, 2005); and Committee and Business Meetings. This on-line program will be updated frequently to reflect the most current revisions.

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Activity Number:	364
Type:	Contributed
Date/Time:	Wednesday, August 10, 2005 : 8:30 AM to 10:20 AM
Sponsor:	General Methodology
Abstract - #304217
Title:	Diagnostics for Machine Learning: Generalizing the Functional ANOVA
Author(s):	Giles Hooker*+
Companies:	McGill University
Address:	1205 Rue Dr Penfield, Dept Psychology, Montreal, H3A 1B1, Canada
Keywords:	Functional ANOVA ; Machine Learning ; Diagnostics
Abstract:	The functional ANOVA has been a widely used and studied construction in statistics throughout the past 50 years. It provides a method of analyzing high-dimensional functions in terms of low-dimensional components and has been used in the literature on machine learning and Monte Carlo quadrature. However, the functional ANOVA is defined only by integration against a uniform measure on the unit cube. Therefore, it can distort the representation of functional dynamics when this measure is not appropriate. This is the case in providing diagnostic tools for machine learning. While the functional ANOVA can be generalized to use a product of univariate measures, doing this this still can be highly distortional. This talk presents a generalization of the functional ANOVA that allows any density function as an underlying measure. The key to the generalization is to estimate the functional effects jointly, rather than individually. We present approximation schemes for the generalized effects and provide an analysis of its use in diagnostic tools for machine learning.

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