相关论文: Extrinsic Kernel Ridge Regression Classifier for P…

Deep kernel learning combines the non-parametric flexibility of kernel methods with the inductive biases of deep learning architectures. We propose a novel deep kernel learning model and stochastic variational inference procedure which…

Recently, machine learning had a remarkable impact, from scientific to everyday-life applications. However, complex tasks often imply unfeasible energy and computational power consumption. Quantum computation might lower such requirements,…

Conditional expectiles are becoming an increasingly important tool in finance as well as in other areas of applications. We analyse a support vector machine type approach for estimating conditional expectiles and establish learning rates…

Thanks to their easy implementation via Radial Basis Functions (RBFs), meshfree kernel methods have been proved to be an effective tool for e.g. scattered data interpolation, PDE collocation, classification and regression tasks. Their…

``Benign overfitting'', the ability of certain algorithms to interpolate noisy training data and yet perform well out-of-sample, has been a topic of considerable recent interest. We show, using a fixed design setup, that an important class…

Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel based methods for additive models. These learning rates compare favourably in particular in high dimensions to…

Kernel methods such as kernel ridge regression and Gaussian process regressions with Matern type kernels have been increasingly used, in particular, to fit potential energy surfaces (PES) and density functionals, and for materials…

This paper addresses distributed learning of a complex object for multiple networked robots based on distributed optimization and kernel-based support vector machine. In order to overcome a fundamental limitation of polynomial kernels…

This paper investigates the robustness and optimality of the multi-kernel correntropy (MKC) on linear regression. We first derive an upper error bound for a scalar regression problem in the presence of arbitrarily large outliers and reveal…

The 3D Gaussian splatting method has drawn a lot of attention, thanks to its high performance in training and high quality of the rendered image. However, it uses anisotropic Gaussian kernels to represent the scene. Although such…

On Euclidean spaces, the Gaussian kernel is one of the most widely used kernels in applications. It has also been used on non-Euclidean spaces, where it is known that there may be (and often are) scale parameters for which it is not…

Quantum kernel methods have emerged as a promising approach for leveraging high-dimensional feature spaces in machine learning, particularly in domains where classical kernel methods face scalability limitations. In this work, we present…

Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…

Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…

Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections,…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

Collaborative representation-based classification (CRC) has demonstrated remarkable progress in the past few years because of its closed-form analytical solutions. However, the existing CRC methods are incapable of processing the nonlinear…

Imputation is a popular technique for handling missing data. We consider a nonparametric approach to imputation using the kernel ridge regression technique and propose consistent variance estimation. The proposed variance estimator is based…