Related papers: Expected Value of Matrix Quadratic Forms with Wish…
The quantum algorithms for Monte Carlo integration (QMCI), which are based on quantum amplitude estimation (QAE), speed up expected value calculation compared with classical counterparts, and have been widely investigated along with their…
This paper deals with the Elliptical Wishart and Inverse Elliptical Wishart distributions, which play a major role when handling covariance matrices. Similarly to multivariate elliptical distributions, these form a large family of…
Measuring expectation values of observables is an essential ingredient in variational quantum algorithms. A practical obstacle is the necessity of a large number of measurements for statistical convergence to meet requirements of precision,…
A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…
We study the problem of estimating the diagonal of an implicitly given matrix $\Ab$. For such a matrix we have access to an oracle that allows us to evaluate the matrix quadratic form $ \ub^\top \Ab \ub$. Based on this query oracle, we…
Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of…
Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class…
A novel algorithm for the computation of the quadratic numerical range is presented and exemplified yielding much better results in less time compared to the random vector sampling method. Furthermore, a bound on the probability for the…
We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…
Two-stage stochastic programming is a problem formulation for decision-making under uncertainty. In the first stage, the actor makes a best "here and now" decision in the presence of uncertain quantities that will be resolved in the future,…
In this paper, we obtain a property of the expectation of the inverse of compound Wishart matrices which results from their orthogonal invariance. Using this property as well as results from random matrix theory (RMT), we derive the…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
We express the probabilistic character associated to the wave function by treating it as a stochastic variable. This is accomplished by means of a stochastic equation for the wave function whose noise changes the phase of the wave function…
Based on a student research project this article gives a short review on Wishart processes. A Wishart procces is a matrix valued continuous time stochastic process with a marginal Wishart distribution. The Wishart distribution is a matrix…
Three classes of stochastic networks and their performance measures are considered. These performance measures are defined as the expected value of some random variables and cannot normally be obtained analytically as functions of network…
We present an analytic method to determine spectral properties of the covariance matrices constructed of correlated Wishart random matrices. The method gives, in the limit of large matrices, exact analytic relations between the spectral…