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...

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...

Pose variation is one of the challenging factors for face recognition. In this paper, we propose a novel cross-pose face recognition method named as Regularized Latent Least Square Regression (RLLSR). The basic assumption is that the images captured under different poses of one person can be viewed as pose-specific transforms of a single ideal object. We treat the observed images as regressor, ...

Weighted least squares support vector machine (WLSSVM) is a robust version of least squares support vector machine (LS-SVM). It adds weights on error variables to eliminate the influence of outliers. But the weights, which largely depend on the original regression errors from unweighted LS-SVM, might be unreliable for correcting the biased estimation of LS-SVM, especially for the training data ...

and Applied Analysis 3 Theorem 4. Suppose that the unbounded hypothesis with p > 2 holds, L−r K f ρ ∈ L 2 ρX (X) for some r > 0, and theα-mixing coefficients satisfy a polynomial decay, that is, α l ≤ bl −t for some b > 0 and t > 0. Then, for any 0 < η < 1, one has with confidence 1 − η, 󵄩 󵄩 󵄩 󵄩 󵄩 fz,γ − ρ 󵄩 󵄩 󵄩 󵄩 󵄩ρX = O(m −θmin{(p−2)t/p,1} (logm)1/2) , (13) where θ is given by θ = { { { { { {...

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...

Abstract. This paper presents a new algorithm to perform regression estimation, in both the inductive and transductive setting. The estimator is defined as a linear combination of functions in a given dictionary. Coefficients of the combinations are computed sequentially using projection on some simple sets. These sets are defined as confidence regions provided by a deviation (PAC) inequality o...