相关论文: Weighted uniform consistency of kernel density est…
The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…
An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness…
Kernel-based modal statistical methods include mode estimation, regression, and clustering. Estimation accuracy of these methods depends on the kernel used as well as the bandwidth. We study effect of the selection of the kernel function to…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
Persistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discrete multisets of points in the plane $\mathbb{R}^2$ that can…
This work explores new classes of nonstationary stochastic sequences associated with polynomial hypergroups. Their covariance structures are analyzed through positive definite kernels and corresponding Hilbert spaces. Novel consistent…
Density estimation plays a fundamental role in many areas of statistics and machine learning. Parametric, nonparametric and semiparametric density estimation methods have been proposed in the literature. Semiparametric density models are…
In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to exibly combine individual regression estimators $r_1, \ldots, r_M$ using a weighted average where the weights are dened based on…
We study the problem of estimating linear response statistics under external perturbations using time series of unperturbed dynamics. Based on the fluctuation-dissipation theory, this problem is reformulated as an unsupervised learning task…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
A hybrid estimator of the log-spectral density of a stationary time series is proposed. First, a multiple taper estimate is performed, followed by kernel smoothing the log-multitaper estimate. This procedure reduces the expected mean square…
The problem of estimation of density functionals like entropy and mutual information has received much attention in the statistics and information theory communities. A large class of estimators of functionals of the probability density…
In this paper, we study the convergence of the spectral embeddings obtained from the leading eigenvectors of certain similarity matrices to their population counterparts. We opt to study this convergence in a uniform (instead of average)…
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…
The paper deals with the density estimation on Rd under sup- norm loss. We provide with fully data-driven estimation procedure and establish for it so called sup-norm oracle inequality. The pro- posed estimator allows to take into account…
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…
We focus on the nonparametric density estimation problem with directional data. We propose a new rule for bandwidth selection for kernel density estimation. Our procedure is automatic, fully data-driven and adaptive to the smoothness degree…
Kernel methods have been widely applied to machine learning and other questions of approximating an unknown function from its finite sample data. To ensure arbitrary accuracy of such approximation, various denseness conditions are imposed…
We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical…
We present a new smooth, Gaussian-like kernel that allows the kernel density estimate for an angular distribution to be exactly represented by a finite number of its Fourier series coefficients. Distributions of angular quantities, such as…