We consider the application of a popular penalised regression method, Ridge Regression, to data with very high dimensions and many more covariates than observations. Our motivation is the problem of out-of-sample prediction and the setting is high-density genotype data from a genome-wide association or resequencing study. Ridge regression has previously been shown to offer improved performance ...

We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a principal component analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that the risk of this ordinary least squares method (PCA-OLS) is within a constant...

This paper considers optimization of the ridge parameters in generalized ridge regression (GRR) by minimizing a model selection criterion. GRR has a major advantage over ridge regression (RR) in that a solution to the minimization problem for one model selection criterion, i.e., Mallows’ Cp criterion, can be obtained explicitly with GRR, but such a solution for any model selection criteria, e.g...

Diuretic activity [ p(1/C)] of benzene sulfonamides was modeled using 13 C NMR chemical shift ( as a molecular descriptor. The regression analyses were carried out using regular as well as Ridge multiple regression analyses. Application of variety of statistics namely ( statistics, Ridge regression and parameter derived there were used for modeling the diuretic activity. Results have shown that...

The two-group cross-validation classification accuracies of six algorithms (i.e., least squares, ridge regression, principal components, a common factor method, equal weighting, and logistic regression) were compared as a function of degree of validity concentration, group separation, and number of subjects. Therein, the findings of two previous studies were extended to the latter three methods...

Fitting quantitative structure-activity relationships (QSAR) requires different statistical methodologies and, to some degree, philosophies depending on the "shape" of the data matrix. When few features are used and there are many compounds, it is a reasonable expectation that good feature subset selection may be made and that nonlinearities and nonadditivities can be detected and diagnosed. Wh...

We introduce an efficient parallel implementation of a Kernel Ridge Regression solver, based on the Gaussian Belief Propagation algorithm (GaBP). Our approach can be easily used in Peer-to-Peer and grid environments, where there is no central authority that allocates work. Empirically, our solver has high accuracy in solving classification problems. We have tested our distributed implementation...

In this paper, regression analysis method i.e., traditional method and ridge regression is applied on the dataset collected for the prediction of compressive strength of concrete. When regression analysis is applied and data set is increased or decreased, the regression coefficients have drastically changed their values like the negative coefficients changed to positive or vice versa. So, tradi...