Sufficient dimension reduction methods provide effective ways to visualize discriminant analysis problems. For example, Cook and Yin (2001) showed that the dimension reduction method of sliced average variance estimation (save) identifies variates that are equivalent to a quadratic discriminant analysis (qda) solution. This article makes this connection explicit to motivate the use of save vari...

Sufficient dimension reduction (sdr) is an effective tool for reducing highdimensional predictor spaces in regression problems. sdr achieves dimension reduction without loss of any regression information and without the need to assume any particular parametric form of a model. This is particularly useful for high-dimensional applications such as data mining, marketing, and bioinformatics. Howev...

Externalism about psychological kinds is the thesis that certain of a subject's mental states and events are dependent for their individuation on the subject's environment. The thesis opens up the possibility that a subject's mental state and event kinds might vary with variations in the subject's environment, even while her physical properties, including her functional properties and her physi...

constipation isa common clinical problem that can be functional or organic in origin. thiscondition sometimes overlaps with irritable bowel syndrome. initially, theclinician should differentiate between true and false constipation by clinicaland preclinical evidence such as colonic transit time. numerous patients believethat all defecation problems are called constipation and use laxatives with...

counterfactual analysis is concerned with explaining events that have not happened. counterfactuals are mental experiments through which one can reconstruct hypothetical versions of the history in one’s mind; these versions are relatively different from the real history, but provide one with the opportunity to test historical hypotheses against the available evidence. historicist researchers in...

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...

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...

The importance of developing artificial media that can be used in the place of serum for maintaining the life of tissues and organs outside the body hardly needs to be emphasized. Many of the studies for which the organ culture technique 1 was developed, as well as others that can be carried on by the simpler methods of tissue culture, depend for their success on the creation of suitable artifi...