Related papers: Kernel Least Mean Square with Adaptive Kernel Size

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…

Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…

Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast…

Kernel ridge regression (KRR) is widely used for nonparametric regression over reproducing kernel Hilbert spaces. It offers powerful modeling capabilities at the cost of significant computational costs, which typically require $O(n^3)$…

Nowadays, with the development of multi-sensor networks, the distributed cubature Kalman filter is one of the well-known existing schemes for state estimation, for which the influence of the non-Gaussian noise, abnormal data, and…

This paper presents an intuitive application of multivariate kernel density estimation (KDE) for data correction. The method utilizes the expected value of the conditional probability density function (PDF) and a credible interval to…

Although multi-view unsupervised feature selection (MUFS) has demonstrated success in dimensionality reduction for unlabeled multi-view data, most existing methods reduce feature redundancy by focusing on linear correlations among features…

The so-called constrained least mean-square algorithm is one of the most commonly used linear-equality-constrained adaptive filtering algorithms. Its main advantages are adaptability and relative simplicity. In order to gain analytical…

Gaussian process regression generally does not scale to beyond a few thousands data points without applying some sort of kernel approximation method. Most approximations focus on the high eigenvalue part of the spectrum of the kernel…

Kernel ridge regression is an important nonparametric method for estimating smooth functions. We introduce a new set of conditions, under which the actual rates of convergence of the kernel ridge regression estimator under both the L_2 norm…

We present a general nonlinear Bayesian filter for high-dimensional state estimation using the theory of reproducing kernel Hilbert space (RKHS). Applying kernel method and the representer theorem to perform linear quadratic estimation in a…

The runtime for Kernel Partial Least Squares (KPLS) to compute the fit is quadratic in the number of examples. However, the necessity of obtaining sensitivity measures as degrees of freedom for model selection or confidence intervals for…

Stochastic configuration networks (SCNs), as a class of randomized learner models, are featured by its way of random parameters assignment in the light of a supervisory mechanism, resulting in the universal approximation property at…

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…

Under the reproducing kernel Hilbert spaces (RKHS), we consider the penalized least-squares of the partially functional linear models (PFLM), whose predictor contains both functional and traditional multivariate parts, and the multivariate…

We consider a distributed learning approach in supervised learning for a large class of spectral regularization methods in an RKHS framework. The data set of size n is partitioned into $m=O(n^\alpha)$ disjoint subsets. On each subset, some…

We develop a novel framework for sparse multiscale kernel approximation of large scattered data problems based on a samplet representation. Samplets form a multiresolution analysis of localized discrete signed measures and enable…

Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…

Gaussian Radial Basis Function (RBF) Kernels are the most-often-employed kernels in artificial intelligence and machine learning routines for providing optimally-best results in contrast to their respective counter-parts. However, a little…

Statistical machine learning plays an important role in modern statistics and computer science. One main goal of statistical machine learning is to provide universally consistent algorithms, i.e., the estimator converges in probability or…