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...

Regression is the study of the dependence of a response variable on a collection predictors collected in . In dimension reduction regression, we seek to find a few linear combinations , such that all the information about the regression is contained in these linear combinations. If is very small, perhaps one or two, then the regression problem can be summarized using simple graphics; for exampl...

A new method is developed for performing sufficient dimension reduction when probabilistic graphical models are being used to estimate parameters. The procedure enriches the domain of application techniques settings where (i) p number variables in model much larger than available sample size n, (ii) slices H uses and (iii) D projection vectors can be H. methodology case sliced inverse regressio...

We developed localized sliced inverse regression for supervised dimension reduction. It has the advantages of preventing degeneracy, increasing estimation accuracy, and automatic subclass discovery in classification problems. A semisupervised version is proposed for the use of unlabeled data. The utility is illustrated on simulated as well as real data sets.

Sliced Inverse Regression (SIR) has been extensively used to reduce the dimension of the predictor space before performing regression. SIR is originally a model free method but it has been shown to actually correspond to the maximum likelihood of an inverse regression model with Gaussian errors. This intrinsic Gaussianity of standard SIR may explain its high sensitivity to outliers as observed ...