Related papers: Sampling Spiked Wishart Eigenvalues
We study the computational task of detecting and estimating correlated signals in a pair of spiked matrices $$ X=\tfrac{\lambda}{\sqrt{n}} xu^{\top}+W, \quad Y=\tfrac{\mu}{\sqrt{n}} yv^{\top}+Z $$ where the spikes $x,y$ have correlation…
In this paper we relate the matrix $S_B$ of the second moments of a spherically truncated normal multivariate to its full covariance matrix $\Sigma$ and present an algorithm to invert the relation and reconstruct $\Sigma$ from $S_B$. While…
In this paper we show that the empirical eigenvalue distribution of any sample covariance matrix generated by independent copies of a stationary regular sequence has a limiting distribution depending only on the spectral density of the…
In this paper, we consider a data matrix $X\in\mathbb{C}^{N\times M}$ where all the columns are i.i.d. samples being $N$ dimensional complex Gaussian of mean zero and covariance $\Sigma\in\mathbb{C}^{N\times N}$. Here the population matrix…
To explore the limits of a stochastic gradient method, it may be useful to consider an example consisting of an infinite number of quadratic functions. In this context, it is appropriate to determine the expected value and the covariance…
We show how the replica method can be used to compute the asymptotic eigenvalue spectrum of a real Wishart product matrix. For unstructured factors, this provides a compact, elementary derivation of a polynomial condition on the Stieltjes…
We discuss an application of the random matrix theory in the context of estimating the bipartite entanglement of a quantum system. We discuss how the Wishart ensemble (the earliest studied random matrix ensemble) appears in this quantum…
We introduce a stochastic process with Wishart marginals: the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary dependent variable. We use it to model dynamic (e.g. time…
In this paper, we want to show the Restricted Wishart distribution is equivalent to the LKJ distribution, which is one way to specify a uniform distribution from the space of positive definite correlation matrices. Based on this theorem, we…
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…
Wishart correlation matrices are the standard model for the statistical analysis of time series. The ensemble averaged eigenvalue density is of considerable practical and theoretical interest. For complex time series and correlation…
We study estimation of the covariance matrix under relative condition number loss $\kappa(\Sigma^{-1/2} \hat{\Sigma} \Sigma^{-1/2})$, where $\kappa(\Delta)$ is the condition number of matrix $\Delta$, and $\hat{\Sigma}$ and $\Sigma$ are the…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
We investigate the asymptotic behavior of the empirical eigenvalues distribution of the partial transpose of a random quantum state. The limiting distribution was previously investigated via Wishart random matrices indirectly (by…
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…
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,…
This paper addresses the asymptotic behavior of a particular type of information-plus-noise-type matrices, where the column and row number of the matrices are large and of the same order, while signals are diverged and time delays of the…
We propose a covariate-dependent discrete graphical model for capturing dynamic networks among discrete random variables, allowing the dependence structure among vertices to vary with covariates. This discrete dynamic network encompasses…
Recently, inference about high-dimensional integrated covariance matrices (ICVs) based on noisy high-frequency data has emerged as a challenging problem. In the literature, a pre-averaging estimator (PA-RCov) is proposed to deal with the…
In this paper we study random matrix models where the matrices in question contain infinitely many spikes. Recent work has characterized the possible outliers in the spectrum of large deformed unitarily invariant models when the number of…