Related papers: Learning "best" kernels from data in Gaussian proc…
Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel data analysis framework with…
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…
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-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high…
We implemented a geometry optimizer based on Gaussian process regression (GPR) to find minimum structures on potential energy surfaces. We tested both a two times differentiable form of the Mat\'{e}rn kernel and the squared exponential…
Kernel Adaptive Filtering (KAF) are mathematically principled methods which search for a function in a Reproducing Kernel Hilbert Space. While they work well for tasks such as time series prediction and system identification they are…
Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
We provide guarantees for approximate Gaussian Process (GP) regression resulting from two common low-rank kernel approximations: based on random Fourier features, and based on truncating the kernel's Mercer expansion. In particular, we…
We provide guarantees for approximate Gaussian Process (GP) regression resulting from two common low-rank kernel approximations: based on random Fourier features, and based on truncating the kernel's Mercer expansion. In particular, we…
Kernel ridge regression (KRR) is a well-known and popular nonparametric regression approach with many desirable properties, including minimax rate-optimality in estimating functions that belong to common reproducing kernel Hilbert spaces…
This paper focuses on parameter selection issues of kernel ridge regression (KRR). Due to special spectral properties of KRR, we find that delicate subdivision of the parameter interval shrinks the difference between two successive KRR…
This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…
Kernel-based statistical methods are efficient, but their performance depends heavily on the selection of kernel parameters. In literature, the optimization studies on kernel-based chemometric methods is limited and often reduced to grid…
The empirical success of deep convolutional networks on tasks involving high-dimensional data such as images or audio suggests that they can efficiently approximate certain functions that are well-suited for such tasks. In this paper, we…
The kernel herding algorithm is used to construct quadrature rules in a reproducing kernel Hilbert space (RKHS). While the computational efficiency of the algorithm and stability of the output quadrature formulas are advantages of this…
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…
This paper presents a method for building a preconditioner for a kernel ridge regression problem, where the preconditioner is not only effective in its ability to reduce the condition number substantially, but also efficient in its…
In $\mathbb R^d$, it is well-known that cumulants provide an alternative to moments that can achieve the same goals with numerous benefits such as lower variance estimators. In this paper we extend cumulants to reproducing kernel Hilbert…
This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression under the covariate shift assumption, utilizing vector-valued reproducing kernel Hilbert spaces (vRKHS). Covariate…