Related papers: KF-PLS: Optimizing Kernel Partial Least-Squares (K…
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…
The kernel least-mean-square (KLMS) algorithm is an appealing tool for online identification of nonlinear systems due to its simplicity and robustness. In addition to choosing a reproducing kernel and setting filter parameters, designing a…
Partial least squares regression---or PLS---is a multivariate method in which models are estimated using either the SIMPLS or NIPALS algorithm. PLS regression has been extensively used in applied research because of its effectiveness in…
Partial Least Squares (PLS) methods have been heavily exploited to analyse the association between two blocs of data. These powerful approaches can be applied to data sets where the number of variables is greater than the number of…
We present a new framework for online Least Squares algorithms for nonlinear modeling in RKH spaces (RKHS). Instead of implicitly mapping the data to a RKHS (e.g., kernel trick), we map the data to a finite dimensional Euclidean space,…
This paper investigates some theoretical properties of the Partial Least Square (PLS) method. We focus our attention on the single component case, that provides a useful framework to understand the underlying mechanism. We provide a…
Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its…
Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…
The kernel least mean squares (KLMS) algorithm is a computationally efficient nonlinear adaptive filtering method that "kernelizes" the celebrated (linear) least mean squares algorithm. We demonstrate that the least mean squares algorithm…
Kernel Regularized Least Squares (KRLS) is a popular method for flexibly estimating models that may have complex relationships between variables. However, its usefulness to many researchers is limited for two reasons. First, existing…
Latent structure methods, specifically linear continuous latent structure methods, are a type of fundamental statistical learning strategy. They are widely used for dimension reduction, regression and prediction, in the fields of…
Many studies collect data that can be considered as a realization of a point process. Included are medical imaging data where photon counts are recorded by a gamma camera from patients being injected with a gamma emitting tracer. It is of…
We propose a novel method to model nonlinear regression problems by adapting the principle of penalization to Partial Least Squares (PLS). Starting with a generalized additive model, we expand the additive component of each variable in…
Signal processing tasks as fundamental as sampling, reconstruction, minimum mean-square error interpolation and prediction can be viewed under the prism of reproducing kernel Hilbert spaces. Endowing this vantage point with contemporary…
High-dimensional compositional data are commonplace in the modern omics sciences amongst others. Analysis of compositional data requires a proper choice of orthonormal coordinate representation as their relative nature is not compatible…
This paper considers the partially functional linear model (PFLM) where all predictive features consist of a functional covariate and a high dimensional scalar vector. Over an infinite dimensional reproducing kernel Hilbert space, the…
Multiple kernel methods less consider the intrinsic manifold structure of multiple kernel data and estimate the consensus kernel matrix with quadratic number of variables, which makes it vulnerable to the noise and outliers within multiple…
Kernel power $k$-means (KPKM) leverages a family of means to mitigate local minima issues in kernel $k$-means. However, KPKM faces two key limitations: (1) the computational burden of the full kernel matrix restricts its use on extensive…
Inspired by kernel methods that have been used extensively in achieving efficient facial animation retargeting, this paper presents a solution to retargeting facial animation in virtual character's face model based on the kernel projection…
We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains…