Related papers: Multivariate Smoothing via the Fourier Integral Th…
Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…
We introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproducing kernel. Our construction extends classical wavelets as…
In the present paper we consider the initial data, external force, viscosity coefficients, and heat conductivity coefficient as random data for the compressible Navier--Stokes--Fourier system. The Monte Carlo method, which is frequently…
We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
We consider the $\mathcal{H}^2$-formatted compression and computational estimation of covariance functions on a compact set in $\mathbb{R}^d$. The classical sample covariance or Monte Carlo estimator is prohibitively expensive for many…
We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density…
A non-parametric extension of control variates is presented. These leverage gradient information on the sampling density to achieve substantial variance reduction. It is not required that the sampling density be normalised. The novel…
This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a…
We deal with the problem of gradient estimation for stochastic differentiable relaxations of algorithms, operators, simulators, and other non-differentiable functions. Stochastic smoothing conventionally perturbs the input of a…
In state space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has…
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…
Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. Drawing upon tools from the multidimensional calculus of variations, we derive an optimal weight function that reduces bias…
In this paper we focus on efficient implementations of the Multivariate Decomposition Method (MDM) for approximating integrals of $\infty$-variate functions. Such $\infty$-variate integrals occur for example as expectations in uncertainty…
Despite more than 40 years of research in condensed-matter physics, state-of-the-art approaches for simulating the radial distribution function (RDF) g(r) still rely on binning pair-separations into a histogram. Such methods suffer from…
A new data-based smoothing parameter for circular kernel density (and its derivatives) estimation is proposed. Following the plug-in ideas, unknown quantities on an optimal smoothing parameter are replaced by suitable estimates. This paper…
Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow,…
We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the systematic use of the $L^2$-flattening theorem obtained in…
In this paper we show how to use Fourier transform methods to analyze the asymptotic behavior of kernel distribution function estimators. Exact expressions for the mean integrated squared error in terms of the characteristic function of the…
Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…