Related papers: James-Stein Estimation in Quantum Gaussian Sensing
We tackle the problem of the estimation of a vector of means from a single vector-valued observation $y$. Whereas previous work reduces the size of the estimates for the largest (absolute) sample elements via shrinkage (like James-Stein) or…
Headline constraints on cosmological parameters from current weak lensing surveys are derived from two-point statistics that are known to be statistically sub-optimal, even in the case of Gaussian fields. We study the performance of a new…
We consider parameter estimation in finite hidden state space Markov models with time-dependent inhomogeneous noise, where the inhomogeneity vanishes sufficiently fast. Based on the concept of asymptotic mean stationary processes we prove…
We consider the problem of parameter estimation in a partially observed linear Gaussian system with small noises in the state and observation equations. We describe asymptotic properties of the MLE and Bayes estimators in the setting with…
Estimating the frequencies of multiple sinusoids in the presence of AWGN and when the data record is short is commonly accomplished by subspace-based methods such as ESPRIT, MUSIC, Min-Norm, etc. These methods do not assume that the data…
Recall the classical hypothesis testing setting with two convex sets of probability distributions P and Q. One receives either n i.i.d. samples from a distribution p in P or from a distribution q in Q and wants to decide from which set the…
Minimum mean square error (MMSE) estimation of block sparse signals from noisy linear measurements is considered. Unlike in the standard compressive sensing setup where the non-zero entries of the signal are independently and uniformly…
Sampling noisy intermediate-scale quantum devices is a fundamental step that converts coherent quantum-circuit outputs to measurement data for running variational quantum algorithms that utilize gradient and Hessian methods in cost-function…
The estimation of signal parameters using quantized data is a recurrent problem in electrical engineering. As an example, this includes the estimation of a noisy constant value and of the parameters of a sinewave, that is, its amplitude,…
In constrained stochastic optimization, one naturally expects that imposing a stricter feasible set does not increase the statistical risk of an estimator defined by projection onto that set. In this paper, we show that this intuition can…
Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE)…
We study the problem of high-dimensional covariance estimation under the constraint that the partial correlations are nonnegative. The sign constraints dramatically simplify estimation: the Gaussian maximum likelihood estimator is well…
We consider a general multivariate model where univariate marginal distributions are known up to a parameter vector and we are interested in estimating that parameter vector without specifying the joint distribution, except for the…
In this paper, we consider the problem of parameter estimating for a family of exponential distributions. We develop the improved estimation method, which generalized the James--Stein approach for a wide class of distributions. The proposed…
A simple yet efficient method of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and…
Quantum estimation theory is a reformulation of random statistical theory with the modern language of quantum mechanics. In fact, the density operator plays a role similar to that of probability distribution functions in classical…
Quantum scale estimation, as introduced and explored here, establishes the most precise framework for the estimation of scale parameters that is allowed by the laws of quantum mechanics. This addresses an important gap in quantum metrology,…
Estimating mutual information (MI) from samples is a fundamental problem in statistics, machine learning, and data analysis. Recently it was shown that a popular class of non-parametric MI estimators perform very poorly for strongly…
Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this…
Achieving quantum-enhanced performances when measuring unknown quantities requires developing suitable methodologies for practical scenarios, that include noise and the availability of a limited amount of resources. Here, we report on the…