Related papers: Bandwidth Selection for Gaussian Kernel Ridge Regr…
We propose a flexible nonparametric regression method for ultrahigh-dimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression. Then, an iterative…
Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear…
We present a novel approach to learn a kernel-based regression function. It is based on the useof conical combinations of data-based parameterized kernels and on a new stochastic convex optimization procedure of which we establish…
Hamilton-Jacobi reachability methods for safety-critical control have been well studied, but the safety guarantees derived rely on the accuracy of the numerical computation. Thus, it is crucial to understand and account for any inaccuracies…
We consider the joint inference of regression coefficients and the inverse covariance matrix for covariates in high-dimensional probit regression, where the predictors are both relevant to the binary response and functionally related to one…
In a Bayesian learning setting, the posterior distribution of a predictive model arises from a trade-off between its prior distribution and the conditional likelihood of observed data. Such distribution functions usually rely on additional…
Bayesian optimization with Gaussian processes (GP) is commonly used to optimize black-box functions. The Mat\'ern and the Radial Basis Function (RBF) covariance functions are used frequently, but they do not make any assumptions about the…
Kernel Ridge Regression (KRR) is a simple yet powerful technique for non-parametric regression whose computation amounts to solving a linear system. This system is usually dense and highly ill-conditioned. In addition, the dimensions of the…
Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…
Kernel methods for deconvolution have attractive features, and prevail in the literature. However, they have disadvantages, which include the fact that they are usually suitable only for cases where the error distribution is infinitely…
The most direct way to express arbitrary dependencies in datasets is to estimate the joint distribution and to apply afterwards the argmax-function to obtain the mode of the corresponding conditional distribution. This method is in practice…
In this paper we consider the kernel estimators of a distribution function defined by the stochastic approximation algorithm when the observation are contamined by measurement errors. It is well known that this estimators depends heavily on…
Improvement of statistical learning models in order to increase efficiency in solving classification or regression problems is still a goal pursued by the scientific community. In this way, the support vector machine model is one of the…
We investigate the feature compression of high-dimensional ridge regression using the optimal subsampling technique. Specifically, based on the basic framework of random sampling algorithm on feature for ridge regression and the A-optimal…
Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable selection algorithm shall be flexible, scalable, and with theoretical guarantee, yet most existing algorithms…
Random feature (RF) has been widely used for node consistency in decentralized kernel ridge regression (KRR). Currently, the consistency is guaranteed by imposing constraints on coefficients of features, necessitating that the random…
This paper discusses a special kind of a simple yet possibly powerful algorithm, called single-kernel Gradraker (SKG), which is an adaptive learning method predicting unknown nodal values in a network using known nodal values and the…
In nonparametric regression problems involving multiple predictors, there is typically interest in estimating an anisotropic multivariate regression surface in the important predictors while discarding the unimportant ones. Our focus is on…
In this paper, we deal with nonparametric regression for circular data, meaning that observations are represented by points lying on the unit circle. We propose a kernel estimation procedure with data-driven selection of the bandwidth…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…