Related papers: Optimal bandwidth selection for semi-recursive ker…
This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The…
To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…
We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…
Previous results pertaining to algebraic state and parameter estimation of linear systems based on a special construction of a forward-backward kernel representation of linear differential invariants are extended to handle large noise in…
The bandwidth of a kernel function is a crucial parameter in the mean shift algorithm. This paper proposes a novel adaptive bandwidth strategy which contains three main contributions. (1) The differences among different adaptive bandwidth…
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…
Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…
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…
It is shown that, for kernel-based classification with univariate distributions and two populations, optimal bandwidth choice has a dichotomous character. If the two densities cross at just one point, where their curvatures have the same…
We develop and analyze a principled approach to kernel ridge regression under covariate shift. The goal is to learn a regression function with small mean squared error over a target distribution, based on unlabeled data from there and…
Kernel ridge regression (KRR) is widely used for nonparametric regression over reproducing kernel Hilbert spaces. It offers powerful modeling capabilities at the cost of significant computational costs, which typically require $O(n^3)$…
We consider the problem of regularized regression in a network of communication-constrained devices. Each node has local data and objectives, and the goal is for the nodes to optimize a global objective. We develop a distributed…
We consider nonparametric estimation of the derivative of a probability density function with the bounded support on $[0,\infty)$. Estimates are looked up in the class of estimates with asymmetric gamma kernel functions. The use of gamma…
In this work, we develop a simple algorithm for semi-supervised regression. The key idea is to use the top eigenfunctions of integral operator derived from both labeled and unlabeled examples as the basis functions and learn the prediction…
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…
Nonparametric methods have been very popular in the last couple of decades in time series and regression, but no such development has taken place for spatial models. A rather obvious reason for this is the curse of dimensionality. For…
We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and $\varepsilon$-support vector regression. By assuming the ground-truth…
Kernel density estimation is a well known method involving a smoothing parameter (the bandwidth) that needs to be tuned by the user. Although this method has been widely used the bandwidth selection remains a challenging issue in terms of…
Estimation of a conditional mean (linking a set of features to an outcome of interest) is a fundamental statistical task. While there is an appeal to flexible nonparametric procedures, effective estimation in many classical nonparametric…
A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of…