Related papers: Gaussian Approximation for High-Dimensional $U$-st…
We consider a problem of approximation of $d$-variate functions defined on $\mathbb{R}^d$ which belong to the Hilbert space with tensor product-type reproducing Gaussian kernel with constant shape parameter. Within worst case setting, we…
Kernel expansions are a topic of considerable interest in machine learning, also because of their relation to the so-called feature maps introduced in machine learning. Properties of the associated basis functions and weights (corresponding…
Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…
Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The…
Finding the mode of a high dimensional probability distribution $D$ is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when $D$ is…
We investigate training and using Gaussian kernel SVMs by approximating the kernel with an explicit finite- dimensional polynomial feature representation based on the Taylor expansion of the exponential. Although not as efficient as the…
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…
Semicontinuous outcomes occur frequently in health services, insurance, and cost studies. Standard nonparametric density estimators are not well suited to such data because they do not naturally accommodate the mixed structure, the…
It is well-known that polynomial reproduction is not possible when approximating with Gaussian kernels. Quasi-interpolation schemes have been developed which use a finite number of Gaussians at different scales, which then reproduce…
Gaussian distributions are widely used in Bayesian variational inference to approximate intractable posterior densities, but the ability to accommodate skewness can improve approximation accuracy significantly, when data or prior…
Random linear mappings are widely used in modern signal processing, compressed sensing and machine learning. These mappings may be used to embed the data into a significantly lower dimension while at the same time preserving useful…
We consider learning an unknown target function $f_*$ using kernel ridge regression (KRR) given i.i.d. data $(u_i,y_i)$, $i\leq n$, where $u_i \in U$ is a covariate vector and $y_i = f_* (u_i) +\varepsilon_i \in \mathbb{R}$. A recent string…
Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of…
We show that a tessellation generated by a small number of random affine hyperplanes can be used to approximate Euclidean distances between any two points in an arbitrary bounded set $T$, where the random hyperplanes are generated by…
Gaussian process models typically contain finite dimensional parameters in the covariance function that need to be estimated from the data. We study the Bayesian fixed-domain asymptotics for the covariance parameters in a universal kriging…
We study how the posterior contraction rate under a Gaussian process (GP) prior depends on the intrinsic dimension of the predictors and the smoothness of the regression function. An open question is whether a generic GP prior that does not…
Kernel estimation techniques, such as mean shift, suffer from one major drawback: the kernel bandwidth selection. The bandwidth can be fixed for all the data set or can vary at each points. Automatic bandwidth selection becomes a real…
Density estimation represents one of the most successful applications of Bayesian nonparametrics. In particular, Dirichlet process mixtures of normals are the gold standard for density estimation and their asymptotic properties have been…
Conformal prediction provides distribution-free coverage guaranties for regression; yet existing methods assume Euclidean output spaces and produce prediction regions that are poorly calibrated when responses lie on Riemannian manifolds. We…
In this paper, we consider the nonparametric estimation of the multivariate probability density function and its partial derivative with a support on $[0,\infty)$. To this end we use the class of kernel estimators with asymmetric gamma…