Related papers: Stochastic Estimation with $Z_2$ Noise
We study the problem of estimating functions of a large symmetric matrix $A_n$ when we only have access to a noisy estimate $\hat{A}_n=A_n+\sigma Z_n/\sqrt{n}.$ We are interested in the case that $Z_n$ is a Wigner ensemble and suggest an…
Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…
One of the major challenges in multivariate analysis is the estimation of population covariance matrix from sample covariance matrix (SCM). Most recent covariance matrix estimators use either shrinkage transformations or asymptotic results…
A novel single-frame quaternion estimator processing two vector observations is introduced. The singular cases are examined, and appropriate rotational solutions are provided. Additionally, an alternative method involving sequential…
We present a supervised machine learning-based method using convolutional neural networks to estimate the covariance matrix of Gaussian quantum states in the presence of thermal noise. Unlike computationally intensive density matrix…
The study of the effect of quantum noise on the accuracy of modeling quantum systems on a quantum computer using the Zalka-Wiesner method is carried out. The efficiency of the developed methods and algorithms is demonstrated by the example…
Noise is an unavoidable part of most measurements which can hinder a correct interpretation of the data. Uncertainties propagate in the data analysis and can lead to biased results even in basic descriptive statistics such as the central…
We consider the problem of estimating means of two Gaussians in a 2-Gaussian mixture, which is not balanced and is corrupted by noise of an arbitrary distribution. We present a robust algorithm to estimate the parameters, together with…
We consider the problem of estimating a cloud of points from numerous noisy observations of that cloud after unknown rotations, and possibly reflections. This is an instance of the general problem of estimation under group action,…
Numerical studies of quantum field theories usually rely upon an accurate determination of stochastically estimated correlation functions in order to extract information about the spectrum of the theory and matrix elements of operators. The…
We focus on estimating the integrated covariance of log-price processes in the presence of market microstructure noise. We construct an efficient unbiased estimator for the quadratic covariation of two It\^{o} processes in the case where…
This paper aims to address two fundamental challenges arising in eigenvector estimation and inference for a low-rank matrix from noisy observations: (1) how to estimate an unknown eigenvector when the eigen-gap (i.e. the spacing between the…
Consider the design based situation where an $r$-regular set is sampled on a random lattice. A fast algorithm for estimating the integrated mean curvature based on this observation is to use a weighted sum of $2\times \dotsm \times 2$…
In this paper, we consider the Group Lasso estimator of the covariance matrix of a stochastic process corrupted by an additive noise. We propose to estimate the covariance matrix in a high-dimensional setting under the assumption that the…
As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how…
The problem of low-rank matrix completion with heterogeneous and sub-exponential (as opposed to homogeneous and Gaussian) noise is particularly relevant to a number of applications in modern commerce. Examples include panel sales data and…
We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such…
Standard noise radars, as well as noise-type radars such as quantum two-mode squeezing radar, are characterized by a covariance matrix with a very specific structure. This matrix has four independent parameters: the amplitude of the…
We consider the problem of estimating a rank-1 signal corrupted by structured rotationally invariant noise, and address the following question: how well do inference algorithms perform when the noise statistics is unknown and hence Gaussian…
We demonstrate the quantum mean estimation algorithm on Euclidean lattice field theories. This shows a quadratic advantage over Monte Carlo methods which persists even in presence of a sign problem, and is insensitive to critical slowing…