Related papers: A note on boundary kernels for distribution functi…

Kernel smoothers are considered near the boundary of the interval. Kernels which minimize the expected mean square error are derived. These kernels are equivalent to using a linear weighting function in the local polynomial regression. It…

We propose two new kernel-type estimators of the mean residual life function $m_X(t)$ of bounded or half-bounded interval supported distributions. Though not as severe as the boundary problems in the kernel density estimation, eliminating…

Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a…

We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing…

We investigate a series of learning kernel problems with polynomial combinations of base kernels, which will help us solve regression and classification problems. We also perform some numerical experiments of polynomial kernels with…

In a previous paper, we studied a kernel estimate of the upper edge of a two-dimensional bounded set, based upon the extreme values of a Poisson point process. The initial paper "Geffroy J. (1964) Sur un probl\`eme d'estimation…

Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…

The discrete kernel method was developed to estimate count data distributions, distinguishing discrete associated kernels based on their asymptotic behaviour. This study investigates the class of discrete asymmetric kernels and their…

Prominently used in support vector machines and logistic regressions, kernel functions (kernels) can implicitly map data points into high dimensional spaces and make it easier to learn complex decision boundaries. In this work, by replacing…

Compared to nonparametric estimators in the multivariate setting, kernel estimators for functional data models have a larger order of bias. This is problematic for constructing confidence regions or statistical tests since the bias might…

Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…

Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for…

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…

We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we…

We consider the high order moments estimator of the frontier of a random pair introduced by Girard, S., Guillou, A., Stupfler, G. (2012). {\it Frontier estimation with kernel regression on high order moments}. In the present paper, we show…

Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…

Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…

Radial basis function (RBF) networks are expanded to incorporate quantum kernel functions enabling a new type of hybrid quantum-classical machine learning algorithm. Using this approach, synthetic examples are introduced which allow for…

We address the estimation of "extreme" conditional quantiles i.e. when their order converges to one as the sample size increases. Conditions on the rate of convergence of their order to one are provided to obtain asymptotically Gaussian…

This paper addresses the problem of distributed learning under communication constraints, motivated by distributed signal processing in wireless sensor networks and data mining with distributed databases. After formalizing a general model…