We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are established under a source and an effective dimensionality condition. It is shown both theoretically and in simulations that long range dependence results in slower c...

We consider the problem of translating a given pattern set B of size m, and matching every point of B to some point of a larger ground set A of size n in an injective way, minimizing the sum of the squared distances between matched points. We show that when B can only be translated along a line, there can be at most m(n − m) + 1 different matchings as B moves along the line, and hence the optim...

Analysis of images involving humans is of significant interest in computer vision because problems such as detection, modeling, recognition, and tracking are fundamental to model interactions between people and understand highlevel activities. Visual information contained in images is generally represented using feature descriptors. Many general classes of descriptors have been proposed focusin...

Partial least squares (PLS) estimation of path models has become very popular in IS research, as an alternative to covariance-based methods. PLS path modeling is often referred to as being useful for “predictive” applications. In this work, we investigate the predictive aspects of PLS path modeling and its relation to predictive analytics and predictive assessment. In particular, we compare it ...

Partial least squares (PLS) regression is a powerful and frequently applied technique in multivariate statistical process control when the process variables are highly correlated. Selection of the number of latent variables to build a representative model is an important issue. A metric frequently used by chemometricians for the determination of the number of latent variables is that of Wold’s ...

Partial least squares is a popular method for soft modelling in industrial applications. This paper introduces the basic concepts and illustrates them with a chemometric example. An appendix describes the experimental PLS procedure of SAS/STAT software.

Partial Least Squares Regression (PLSR) is a linear regression technique developed to deal with high-dimensional regressors and one or several response variables. In this paper we introduce robustified versions of the SIMPLS algorithm being the leading PLSR algorithm because of its speed and efficiency. Because SIMPLS is based on the empirical cross-covariance matrix between the response variab...

We present a method for computing partial spectra of Hermitian matrices, based on a combination of subspace iteration with rational filtering. In contrast with classical rational filters derived from Cauchy integrals or from uniform approximations to a step function, we adopt a least-squares (LS) viewpoint for designing filters. One of the goals of the proposed approach is to build a filter tha...

In the machine learning field, feature selection is used to discard the redundant information and improve the learning accuracy. In this paper, the redundant information is reused in the learning of partial least squares method within the frame of multitask learning. This newly proposed method is used to solve the multivariate calibration problem, a classic problem in the analytical chemistry f...

The main contributions of this paper can be summarized as follows. First, we compare the Partial Least Squares (PLS) and the Principal Component Analysis (PCA), under fairly general conditions. (In particular, the existence of a true linear regression is not assumed.) We prove that PLS and PCA are equivalent, to within a rst-order approximation, hence providing a theoretical explanation for emp...