Related papers: epsilon-Samples of Kernels
This paper develops the process of using Richardson Extrapolation to improve the Kernel Density Estimation method, resulting in a more accurate (lower Mean Squared Error) estimate of a probability density function for a distribution of data…
Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…
This work studies the problem of estimating a two-dimensional superposition of point sources or spikes from samples of their convolution with a Gaussian kernel. Our results show that minimizing a continuous counterpart of the $\ell_1$ norm…
Kernel survival analysis models estimate individual survival distributions with the help of a kernel function, which measures the similarity between any two data points. Such a kernel function can be learned using deep kernel survival…
The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…
Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting…
Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \Psi(t) be a positive continuous function such that \|\Psi f^{\beta}\|_{\infty}<\infty for some 0<\beta<1/2. Under natural…
The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…
We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i.e., $n\asymp d^{\gamma}$ for some $\gamma >0$ ). We first build a general tool to…
We focus on the distribution regression problem: regressing to a real-valued response from a probability distribution. Although there exist a large number of similarity measures between distributions, very little is known about their…
The paper addresses the problem to estimate the power spectral density of an ARMA zero mean Gaussian process. We propose a kernel based maximum entropy spectral estimator. The latter searches the optimal spectrum over a class of high order…
We propose a novel kernel-based nonparametric two-sample test, employing the combined use of kernel mean and kernel covariance embedding. Our test builds on recent results showing how such combined embeddings map distinct probability…
Imbalanced response variable distribution is a common occurrence in data science. In fields such as fraud detection, medical diagnostics, system intrusion detection and many others where abnormal behavior is rarely observed the data under…
An exact, closed form, and easy to compute expression for the mean integrated squared error (MISE) of a kernel estimator of a normal mixture cumulative distribution function is derived for the class of arbitrary order Gaussian-based…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…
In this paper, we construct a moment inequality for mixing dependent random variables, it is of independent interest. As applications, the consistency of the kernel density estimation is investigated. Several limit theorems are established:…
This study proposes multivariate kernel density estimation by stagewise minimization algorithm based on $U$-divergence and a simple dictionary. The dictionary consists of an appropriate scalar bandwidth matrix and a part of the original…
We show that common choices of kernel functions for a highly accurate and massively scalable nearest-neighbour based GP regression model (GPnn: \cite{GPnn}) exhibit gradual convergence to asymptotic behaviour as dataset-size $n$ increases.…
Previous work generally believes that improving the spatial invariance of convolutional networks is the key to object counting. However, after verifying several mainstream counting networks, we surprisingly found too strict pixel-level…
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…