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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big BERKELEY-STANFORD SYMPOSIUM}
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\centerline{University of California, Berkeley}
\centerline{4:10 p.m., Tuesday, April 16, 2002}
\centerline{Evans Hall, Room 1011}

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\centerline{\sl Art B. Owen}
\centerline{\sl Stanford University}
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\centerline{\bf Identifying important variables and interactions in black box functions}

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Quasi-Monte Carlo methods have been successfully used to integrate some
very high dimensional functions. Inspection always seems to reveal that
those functions are especially simple, having functional anova
decompositions dominated by main effects and low dimensional interactions.

This talk will present a method for inspecting black box functions to
determine which variables and interactions are most important. The method
is constructive, in that provides a computable approximation to the
function under study. The approach uses a multivariate orthogonal series
expansion of square integrable functions on the unit cube.  The
coefficients are estimated by quasi-regression: a combination of Monte
Carlo sampling and shrinkage.

Though speculative, it is interesting to apply the method to black box
functions from machine learning. Such functions can be
much simpler than their functional forms suggest. The challenge, still not
solved, is to reconcile variable importance determined with respect to a
product measure and data decidedly not from a product measure.

(This talk is based on joint work with Tao Jiang.)

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