This paper describes the application of a combined orthogonal array design and overlapping resolution mapping to the optimization of miceller electrokinetic chromatography for the separation of 10 substituted benzenes. The most important factors were first determined according to an OA16(2(15)) through 16 pre-designed experiments; a second set of experiments was carried out according to a trian...

Least-Angle Regression and the LASSO (`1-penalized regression) offer a number of advantages in variable selection applications over procedures such as stepwise or ridge regression, including prediction accuracy, stability and interpretability. We discuss formulations of these algorithms that extend to datasets in which the number of observations could be so large that it would not be possible t...

We introduce a fast stepwise regression method, called the orthogonal greedy algorithm (OGA), that selects input variables to enter a p-dimensional linear regression model (with p À n, the sample size) sequentially so that the selected variable at each step minimizes the residual sum squares. We derive the convergence rate of OGA and develop a consistent model selection procedure along the OGA ...

We introduce a fast stepwise regression method, called the orthogonal greedy algorithm (OGA), that selects input variables to enter a p-dimensional linear regression model (with p >> n, the sample size) sequentially so that the selected variable at each step minimizes the residual sum squares. We derive the convergence rate of OGA as m = mn becomes infinite, and also develop a consistent model ...

This paper explores linear methods for combining several word embedding models into an ensemble. We construct the combined models using an iterative method based on either ordinary least squares regression or the solution to the orthogonal Procrustes problem. We evaluate the proposed approaches on Estonian—a morphologically complex language, for which the available corpora for training word emb...

Penalized selection criteria like AIC or BIC are among the most popular methods for variable selection. Their theoretical properties have been studied intensively and are well understood, but making use of them in case of high-dimensional data is difficult due to the non-convex optimization problem induced by L0 penalties. In this paper we introduce an adaptive ridge procedure (AR), where itera...

Short-term forecasting of wind generation requires a model of the function for the conversion of meteorological variables (mainly wind speed) to power production. Such a power curve is nonlinear and bounded, in addition to being nonstationary. Local linear regression is an appealing nonparametric approach for power curve estimation, for which the model coefficients can be tracked with recursive...

An orthogonal double cover (ODC) of the complete graph is a collection of graphs such that every two of them share exactly one edge and every edge of the complete graph belongs to exactly two of the graphs. In this paper, we consider the case where the graph to be covered twice is the complete bipartite graph Kmn,mn (for any values ofm,n) and all graphs in the collection are isomorphic to certa...

Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theor...