منابع مشابه
Kernel Dimension Reduction in Regression∗
We present a new methodology for sufficient dimension reduction (SDR). Our methodology derives directly from the formulation of SDR in terms of the conditional independence of the covariate X from the response Y , given the projection of X on the central subspace [cf. J. Amer. Statist. Assoc. 86 (1991) 316–342 and Regression Graphics (1998) Wiley]. We show that this conditional independence ass...
متن کاملRegression on manifolds using kernel dimension reduction
We study the problem of discovering a manifold that best preserves information relevant to a nonlinear regression. Solving this problem involves extending and uniting two threads of research. On the one hand, the literature on sufficient dimension reduction has focused on methods for finding the best linear subspace for nonlinear regression; we extend this to manifolds. On the other hand, the l...
متن کاملGradient-based kernel dimension reduction for regression
This paper proposes a novel approach to linear dimension reduction for regression using nonparametric estimation with positive definite kernels or reproducing kernel Hilbert spaces. The purpose of the dimension reduction is to find such directions in the explanatory variables that explain the response sufficiently: this is called sufficient dimension reduction. The proposed method is based on a...
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Nonparametric regression is a powerful tool to estimate nonlinear relations between some predictors and a response variable. However, when the number of predictors is high, nonparametric estimators may suffer from the curse of dimensionality. In this chapter, we show how a dimension reduction method (namely Sliced Inverse Regression) can be combined with nonparametric kernel regression to overc...
متن کاملCanonical kernel dimension reduction
A new kernel dimension reduction (KDR) method based on the gradient space of canonical functions is proposed for sufficient dimension reduction (SDR). Similar to existing KDR methods, this new method achieves SDR for arbitrary distributions, but with more flexibility and improved computational efficiency. The choice of loss function in cross-validation is discussed, and a two-stage screening pr...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2009
ISSN: 0090-5364
DOI: 10.1214/08-aos637