Related papers: Sampling the eigenvalues of random orthogonal and …
We propose a second-order accurate method to estimate the eigenvectors of extremely large matrices thereby addressing a problem of relevance to statisticians working in the analysis of very large datasets. More specifically, we show that…
We consider $n\times n$ real symmetric and hermitian random matrices $H_{n,m}$ equals the sum of a non-random matrix $H_{n}^{(0)}$ matrix and the sum of $m$ rank-one matrices determined by $m$ i.i.d. isotropic random vectors with…
Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe recently presented a conjectured formula for the distribution of eigenphases of Haar-distributed random SU(N) matrices ($\beta$=2), supported by explicit…
Motivated by a problem in learning theory, we are led to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the derivative of random polynomials (generated by picking their roots…
Hidden Markov Models (HMMs) are one of the most fundamental and widely used statistical tools for modeling discrete time series. In general, learning HMMs from data is computationally hard (under cryptographic assumptions), and…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
This paper gives a rigorous proof of a conjectured statistical self-similarity property of the eigenvalues random matrices from the Circular Unitary Ensemble. We consider on the one hand the eigenvalues of an $n \times n$ CUE matrix, and on…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
We introduce the Hamming Ball Sampler, a novel Markov Chain Monte Carlo algorithm, for efficient inference in statistical models involving high-dimensional discrete state spaces. The sampling scheme uses an auxiliary variable construction…
Let H be a Haar distributed random matrix on the group of pxp real orthogonal matrices. Partition H into four blocks: (1) the (1,1) element, (2)the rest of the first row, (3) the rest of the first column, and (4)the remaining (p-1)x(p-1)…
In this paper, we use the Poincare separation theorem for estimating the eigenvalues of the fine grid. We propose a randomized version of the algorithm where several different coarse grids are constructed thus leading to more comprehensive…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
Estimating properties of unknown unitary operations is a fundamental task in quantum information science. While full unitary tomography requires a number of samples to the unknown unitary scaling linearly with the dimension (implying…
For a matrix ${\bf A}$ with linearly independent columns, this work studies to use its normalization $\bar{\bf A}$ and ${\bf A}$ itself to approximate its orthonormalization $\bf V$. We theoretically analyze the order of the approximation…
In this technical report, we discuss several sampling algorithms for Determinantal Point Processes (DPP). DPPs have recently gained a broad interest in the machine learning and statistics literature as random point processes with negative…
We develop an iterative refinement method that improves the accuracy of a user-chosen subset of $k$ eigenvectors ($k\ll n$) of an $n\times n$ real symmetric matrix. Using an orthogonal matrix represented in compact WY form, the method…
We consider the problem of estimating the principal components of a population correlation matrix from a limited number of measurement data. Using a combination of random matrix and information-theoretic tools, we show that all the…
Efficient schemes for sampling from the eigenvalues of the Wishart distribution have recently been described for both the uncorrelated central case (where the covariance matrix is $\mathbf{I}$) and the spiked Wishart with a single spike…
We investigate the distribution of eigenvalues of weighted adjacency matrices from a specific ensemble of random graphs. We distribute $N$ vertices across a fixed number $\kappa$ of components, with asymptotically $\alpha_j \dot N$ vertices…
The eigenvalue of a Hamiltonian, $\mathcal{H}$, can be estimated through the phase estimation algorithm given the matrix exponential of the Hamiltonian, $exp(-i\mathcal{H})$. The difficulty of this exponentiation impedes the applications of…