Aggregated estimators and empirical complexity for least square regression

Aggregated Estimators and Empirical Complexity for Least Square Regression

Numerous empirical results have shown that combining regression procedures can be a very efficient method. This work provides PAC bounds for the L2 generalization error of such methods. The interest of these bounds are twofold. First, it gives for any aggregating procedure a bound for the expected risk depending on the empirical risk and the empirical complexity measured by the Kullback-Leibler...

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...

Orthogonal Least Square with Boosting for Regression

Regression Modeling for Spherical Data via Non-parametric and Least Square Methods

Introduction Statistical analysis of the data on the Earth's surface was a favorite subject among many researchers. Such data can be related to animal's migration from a region to another position. Then, statistical modeling of their paths helps biological researchers to predict their movements and estimate the areas that are most likely to constitute the presence of the animals. From a geome...

Learning Rates of Least-Square Regularized Regression

This paper considers the regularized learning algorithm associated with the leastsquare loss and reproducing kernel Hilbert spaces. The target is the error analysis for the regression problem in learning theory. A novel regularization approach is presented, which yields satisfactory learning rates. The rates depend on the approximation property and the capacity of the reproducing kernel Hilbert...