Related papers: Expected Value of Matrix Quadratic Forms with Wish…
Many data-analysis problems involve large dense matrices that describe the covariance of stationary noise processes; the computational cost of inverting these matrices, or equivalently of solving linear systems that contain them, is often a…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
Quadratic matrix equations of the kind $A_1X^2+A_0X+A_{-1}=X$ are encountered in the analysis of Quasi--Birth-Death stochastic processes where the solution of interest is the minimal nonnegative solution $G$. In many queueing models,…
It is known that the estimating equations for quantile regression (QR) can be solved using an EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent…
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 present a general method to determine the probability that stochastic Monte Carlo data, in particular those generated in a lattice QCD calculation, would have been obtained were that data drawn from the distribution predicted by a given…
We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…
Uncertainty estimation in large deep-learning models is a computationally challenging task, where it is difficult to form even a Gaussian approximation to the posterior distribution. In such situations, existing methods usually resort to a…
We consider monotone inclusion problems where the operators may be expectation-valued, a class of problems that subsumes convex stochastic optimization problems as well as subclasses of stochastic variational inequality and equilibrium…
Statistical model checking estimates probabilities and expectations of interest in probabilistic system models by using random simulations. Its results come with statistical guarantees. However, many tools use unsound statistical methods…
Covariance matrices play a major role in statistics, signal processing and machine learning applications. This paper focuses on the \textit{semiparametric} covariance/scatter matrix estimation problem in elliptical distributions. The class…
We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the…
We study here the so-called spiked Wigner and Wishart models, where one observes a low-rank matrix perturbed by some Gaussian noise. These models encompass many classical statistical tasks such as sparse PCA, submatrix localization,…
The space of positive definite symmetric matrices has been studied extensively as a means of understanding dependence in multivariate data along with the accompanying problems in statistical inference. Many books and papers have been…
Stochastic iterative methods are useful in a variety of large-scale numerical linear algebraic, machine learning, and statistical problems, in part due to their low-memory footprint. They are frequently used in a variety of applications,…
A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory…
We present a simple Coulomb gas method to calculate analytically the probability of rare events where the maximum eigenvalue of a random matrix is much larger than its typical value. The large deviation function that characterizes this…
We study low-rank matrix estimation for a generic inhomogeneous output channel through which the matrix is observed. This generalizes the commonly considered spiked matrix model with homogeneous noise to include for instance the dense…
Ordinary stochastic neural networks mostly rely on the expected values of their weights to make predictions, whereas the induced noise is mostly used to capture the uncertainty, prevent overfitting and slightly boost the performance through…
We investigate an additive perturbation of a complex Wishart random matrix and prove that a large deviation principle holds for the spectral measures. The rate function is associated to a vector equilibrium problem coming from logarithmic…