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This paper investigates covariance operator estimation via thresholding. For Gaussian random fields with approximately sparse covariance operators, we establish non-asymptotic bounds on the estimation error in terms of the sparsity level of…
In part I, spectral moments and kurtosis were established as parameters in analytic models of correlation and spectral density functions for dynamic reverberation fields. In this part II, several practical limitations affecting the accuracy…
In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular…
Machine-learned regression models represent a promising tool to implement accurate and computationally affordable energy-density functionals to solve quantum many-body problems via density functional theory. However, while they can easily…
Results concerning the construction of quantum Bayesian error regions as a means to certify the quality of parameter point estimators have been reported in recent years. This task remains numerically formidable in practice for large…
From a wavelet analysis, one derives a nonparametrical estimator for the spectral density of a Gaussian process with stationary increments. First, the idealistic case of a continuous time path of the process is considered. A punctual…
It is a typical standard assumption in the density deconvolution problem that the characteristic function of the measurement error distribution is non-zero on the real line. While this condition is assumed in the majority of existing works…
Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the…
This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The…
This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a…
Quantum multiparameter estimation involves estimating multiple parameters simultaneously and can be more precise than estimating them individually. Our interest here is to determine fundamental quantum limits to the achievable…
Speech utterances recorded under differing conditions exhibit varying degrees of confidence in their embedding estimates, i.e., uncertainty, even if they are extracted using the same neural network. This paper aims to incorporate the…
Several recent studies advocate the use of spectral discriminators, which evaluate the Fourier spectra of images for generative modeling. However, the effectiveness of the spectral discriminators is not well interpreted yet. We tackle this…
Weak gravitational lensing observations probe the spectrum and evolution of density fluctuations and the cosmological parameters which govern them. At low redshifts, the non-linear gravitational evolution of large scale structure produces a…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
We analyze four different approaches to estimate a multivariate probability density (or the log-density) and its first and second order derivatives. Two methods, local log-likelihood and local Hyv\"arinen score estimation, are in terms of…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
We develop a method for estimating the shear power spectra from weak lensing observations and test it on simulated data. Our method describes the shear field in terms of angular power spectra and cross correlation of the two shear modes…
This paper proposes a novel, highly effective spectrum sensing algorithm for cognitive radio and whitespace applications. The proposed spectral covariance sensing (SCS) algorithm exploits the different statistical correlations of the…
Uncertainty estimation has been extensively studied in recent literature, which can usually be classified as aleatoric uncertainty and epistemic uncertainty. In current aleatoric uncertainty estimation frameworks, it is often neglected that…