Related papers: Bandwidth selection in deconvolution kernel distri…
The variance reduction established by importance sampling strongly depends on the choice of the importance sampling distribution. A good choice is often hard to achieve especially for high-dimensional integration problems. Nonparametric…
We introduce the data driven extreme value distribution (DDEVD) estimator, a kernel-based method for estimating extreme value distributions from data. We derive its mean integrated squared error (MISE) in detail, use it to compute the…
In this paper, a distributed stochastic approximation algorithm is studied. Applications of such algorithms include decentralized estimation, optimization, control or computing. The algorithm consists in two steps: a local step, where each…
Kernel image regression methods have shown to provide excellent efficiency in many image processing task, such as image and light-field compression, Gaussian Splatting, denoising and super-resolution. The estimation of parameters for these…
Local polynomial regression of order at least one often performs poorly in regions of sparse data. Local constant regression is exceptional in this regard, though it is the least accurate method in general, especially at the boundaries of…
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…
Spanners have been shown to be a powerful tool in graph algorithms. Many spanner constructions use a certain type of clustering at their core, where each cluster has small diameter and there are relatively few spanner edges between…
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…
A mean function in a reproducing kernel Hilbert space (RKHS), or a kernel mean, is central to kernel methods in that it is used by many classical algorithms such as kernel principal component analysis, and it also forms the core inference…
Split sample methods have recently been put forward as a way to reduce the coverage oscillations that haunt confidence intervals for parameters of lattice distributions, such as the binomial and Poisson distributions. We study split sample…
Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…
We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing…
Modern data analyses frequently encounter settings where samples of variables are contaminated by measurement error. Ignoring measurement noise can substantially degrade statistical inference, while existing correction techniques are often…
We investigate the stochastic gradient descent (SGD) method where the step size lies within a banded region instead of being given by a fixed formula. The optimal convergence rate under mild conditions and large initial step size is proved.…
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…
In kernel methods, the median heuristic has been widely used as a way of setting the bandwidth of RBF kernels. While its empirical performances make it a safe choice under many circumstances, there is little theoretical understanding of why…
We deal with parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) with a small dispersion parameter based on high frequency data which are observed in time and space. By using the thinned…
In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or…
We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…
Despite its reduced complexity, lattice reduction-aided decoding exhibits a widening gap to maximum-likelihood (ML) performance as the dimension increases. To improve its performance, this paper presents randomized lattice decoding based on…