Showing papers by "Jerome H. Friedman published in 1989"

Regularized Discriminant Analysis

Abstract: Linear and quadratic discriminant analysis are considered in the small-sample, high-dimensional setting. Alternatives to the usual maximum likelihood (plug-in) estimates for the covariance matrices are proposed. These alternatives are characterized by two parameters, the values of which are customized to individual situations by jointly minimizing a sample-based estimate of future misclassification risk. Computationally fast implementations are presented, and the efficacy of the approach is examined through simulation studies and application to data. These studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved.

Flexible parsimonious smoothing and additive modeling

Abstract: A simple method is presented for fitting regression models that are nonlinear in the explanatory variables. Despite its simplicity—or perhaps because of it—the method has some powerful characteristics that cause it to be competitive with and often superior to more sophisticated techniques, especially for small data sets in the presence of high noise.

Classification: Oldtimers and newcomers

Abstract: Classification and regression techniques are among the most used tools by chemometricians. With classification, the two classic methods are discriminant analysis and SIMCA. In this paper we discuss the connection between these two methods and introduce two new ones of the same family: DASCO (discriminant analysis with shrunken covariances) and RDA (regularized discriminant analysis). We demonstrate on both simulated and real data sets that their performance is superior to the old favorites. This is especially true in small-sample/high-dimension settings typical in chemistry.