Related papers: Spectral Density Estimation for Random Fields via …
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…
We propose computationally efficient methods for estimating stationary multivariate spatial and spatial-temporal spectra from incomplete gridded data. The methods are iterative and rely on successive imputation of data and updating of model…
Accurately estimating data density is crucial for making informed decisions and modeling in various fields. This paper presents a novel nonparametric density estimation procedure that utilizes bivariate penalized spline smoothing over…
We introduce a supervised dimensionality reduction methodology for categorical (and discretized mixed-type) data based on a density-matrix construction induced by class-conditional frequencies. Given a labeled dataset encoded in a one-hot…
Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…
This paper studies density estimation and regression analysis with contaminated data observed on the unit hypersphere S^d. Our methodology and theory are based on harmonic analysis on general S^d. We establish novel nonparametric density…
This paper introduces a novel boundary integral approach of shape uncertainty quantification for the Helmholtz scattering problem in the framework of the so-called parametric method. The key idea is to construct an integration grid whose…
Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
We extend density matrix embedding theory to periodic systems, resulting in an electronic band structure method for solid-state materials. The electron correlation can be captured by means of a local impurity model using various choices of…
In this paper, we propose a convex optimization-based estimation of sparse and smooth power spectral densities (PSDs) of complex-valued random processes from mixtures of realizations. While the PSDs are related to the magnitude of the…
This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized…
Non-parametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these…
We introduce a nonparametric spectral density estimator for continuous-time and continuous-space processes measured at fully irregular locations. Our estimator is constructed using a weighted nonuniform Fourier sum whose weights yield a…
We present a method to derive an upper bound for the entropy density of coupled map lattices with local interactions from local observations. To do this, we use an embedding technique being a combination of time delay and spatial embedding.…
This paper proposes a nonparametric multivariate density forecast model based on deep learning. It not only offers the whole marginal distribution of each random variable in forecasting targets, but also reveals the future correlation…
We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…
This paper addresses the deconvolution problem of estimating a square-integrable probability density from observations contaminated with additive measurement errors having a known density. The estimator begins with a density estimate of the…
We review the problem of how to compute the spectral density of sparse symmetric random matrices, i.e. weighted adjacency matrices of undirected graphs. Starting from the Edwards-Jones formula, we illustrate the milestones of this line of…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…