Efficiency Improvement for Ordinary Least Square and Orthogonal Regression-An Application in Chemical Engineering

Ordinary Least Square Regression, Orthogonal Regression, Geometric Mean Regression and their Applications in Aerosol Science

Abstract. Regression analysis, especially the ordinary least squares method which assumes that errors are confined to the dependent variable, has seen a fair share of its applications in aerosol science. The ordinary least squares approach, however, could be problematic due to the fact that atmospheric data often does not lend itself to calling one variable independent and the other dependent. ...

Orthogonal Least Square with Boosting for Regression

Application of integral operator for regularized least-square regression

In this paper, we study the consistency of the regularized least square regression in a general reproducing kernel Hilbert spaces. We characterized the compactness of the inclusion map from a reproducing kernel Hilbert space to the space of continuous functions and showed that the capacity based analysis by uniform covering numbers may fail in a very general setting. We prove the consistency an...

Application of Partial Least Square Regression in Uncertainty Analysis

The aim of this work is to show how partial least squares (PLS) regression when combined with two other techniques Karhunen-Loeve (KL) expansion and Markov chain Monte Carlo (MCMC) can be efficient and effective at addressing parameter uncertainties that affect the predictive ability of a model for critical applications such as monitoring and control. We introduce a combination of PLS regressio...

Partial Least Square Regression PLS-Regression

PLS regression is a recent technique that generalizes and combines features from principal component analysis and multiple regression. Its goal is to predict or analyze a set of dependent variables from a set of independent variables or predictors. This prediction is achieved by extracting from the predictors a set of orthogonal factors called latent variables which have the best predictive pow...