相关论文: Nonparametric Estimation of Probability Density Fu…

This paper introduces a novel kernel density estimator (KDE) based on the generalised exponential (GE) distribution, designed specifically for positive continuous data. The proposed GE KDE offers a mathematically tractable form that avoids…

We introduce kernel density machines (KDM), an agnostic kernel-based framework for learning the Radon-Nikodym derivative (density) between probability measures under minimal assumptions. KDM applies to general measurable spaces and avoids…

We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and…

We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…

We describe and analyze a simple random feature scheme (RFS) from prescribed compositional kernels. The compositional kernels we use are inspired by the structure of convolutional neural networks and kernels. The resulting scheme yields…

Length-biased data are a particular case of weighted data, which arise in many situations: biomedicine, quality control or epidemiology among others. In this paper we study the theoretical properties of kernel density estimation in the…

Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…

In this work, we establish the asymptotic normality of the deconvolution kernel density estimator in the context of strongly mixing random fields. Only minimal conditions on the bandwidth parameter are required and a simple criterion on the…

Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and…

We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…

A probability density function (pdf) encodes the entire stochastic knowledge about data distribution, where data may represent stochastic observations in robotics, transition state pairs in reinforcement learning or any other empirically…

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…

Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a…

Radiomics involves the study of tumor images to identify quantitative markers explaining cancer heterogeneity. The predominant approach is to extract hundreds to thousands of image features, including histogram features comprised of…

Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy…

We derive concentration inequalities for the supremum norm of the difference between a kernel density estimator (KDE) and its point-wise expectation that hold uniformly over the selection of the bandwidth and under weaker conditions on the…

Nonparametric density estimators are studied for $d$-dimensional, strongly spatial mixing data which is defined on a general $N$-dimensional lattice structure. We consider linear and nonlinear hard thresholded wavelet estimators which are…

In the context of regressing a response $Y$ on a predictor $X$, we consider estimating the local modes of the distribution of $Y$ given $X=x$ when $X$ is prone to measurement error. We propose two nonparametric estimation methods, with one…

Nonparametric density estimation is an unsupervised learning problem. In this work we propose a two-step procedure that casts the density estimation problem in the first step into a supervised regression problem. The advantage is that we…

Kernel density estimation (KDE) stands out as a challenging task in machine learning. The problem is defined in the following way: given a kernel function $f(x,y)$ and a set of points $\{x_1, x_2, \cdots, x_n \} \subset \mathbb{R}^d$, we…