Least square regression with indefinite kernels and coefficient regularization

Regularized Least Square Regression with Spherical Polynomial Kernels

This article considers regularized least square regression on the sphere. It develops a theoretical analysis of the generalization performances of regularized least square regression algorithm with spherical polynomial kernels. The explicit bounds are derived for the excess risk error. The learning rates depend on the eigenvalues of spherical polynomial integral operators and on the dimension o...

Least Square Variational Bayesian Autoencoder with Regularization

In recent years Variation Autoencoders have become one of the most popular unsupervised learning of complicated distributions. Variational Autoencoder (VAE) provides more efficient reconstructive performance over a traditional autoencoder. Variational auto enocders make better approximaiton than MCMC. The VAE defines a generative process in terms of ancestral sampling through a cascade of hidde...

Least Square Regression Learning with Data Dependent Hypothesis and Coefficient Regularzation

-We study the least square regression with data dependent hypothesis and coefficient regularization algorithms based on general kernel. An explicit expression of the solution of this kernel scheme is derived. Then we provide a sample error with a decay of 1 ( ) O m and estimate the approximation error in terms of some kind of K -functional. Index Terms -Least Square Regressions, Data Dependent ...

Orthogonal Least Square with Boosting for Regression

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...