Projection Pursuit Papers Available

[Charles Roosen]

The following Tech Reports are now available by anonymous ftp from
research.att.com.  They are in the directory /dist/trevor as
"asp.tm.ps.Z" and "lrpp.tm.ps.Z".


Charles Roosen
charles at playfair.stanford.edu

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	Automatic Smoothing Spline Projection Pursuit

	Charles Roosen		Trevor Hastie
	Dept. of Stat.		Stat. & Data Analysis Research Dept.
	Stanford U.		AT&T Bell Labs

			Abstract

A highly flexible nonparametric regression model for predicting a
response y given covariates {x_k}_{k=1}^d is the projection pursuit
regression (PPR) model yhat=h(x)=\beta_0 + \sum_j
\beta_j f_j(\alpha_j^T x), where the f_j are general
smooth functions with mean zero and norm one, and \sum_{k=1}^d
\alpha_{kj}^2=1.  The standard PPR algorithm of Friedman
estimates the smooth functions f_j(v_j) using the supersmoother
nonparametric scatterplot smoother.  Friedman's algorithm constructs a
model with M_{max} linear combinations, then prunes back to a
simpler model of size M \leq M_{max}, where M and M_{max} are
specified by the user.  This paper discusses an alternative algorithm
in which the smooth functions are estimated using smoothing
splines, and the number of terms M and M_{max} are chosen by
generalized cross-validation.


	Logistic Response Projection Pursuit

	Charles Roosen		Trevor Hastie
	Dept. of Stat.		Stat. & Data Analysis Research Dept.
	Stanford U.		AT&T Bell Labs

			Abstract

A highly flexible nonparametric regression model for predicting a
response y given covariates x is the projection
pursuit regression (PPR) model yhat=h(x)=\beta_0 + \sum_j
\beta_j f_j(\alpha_j^T x), where the f_j are general
smooth functions with mean zero and norm one, and 
\sum_{k=1}^d \alpha_{kj}^2=1.  With a binary response
$y$, the common approach to fitting a PPR model is to fit yhat to
minimize average squared error without explicitly considering the
binary nature of the response.  We develop an alternative logistic
response projection pursuit model, in which y is take to be
binomial(p), where \log({p \over 1-p})=h(x).  This may be fit
by minimizing either binomial deviance or average squared error.  We
compare the logistic response models to the linear model on simulated
data.

In addition, we develop a generalized projection pursuit framework for
exponential family models.  We also present a smoothing spline based
PPR algorithm, and compare it to supersmoother
and polynomial based PPR algorithms.