Related papers: Optimal Estimation and Rank Detection for Sparse S…
The computation of the sparse principal component of a matrix is equivalent to the identification of its principal submatrix with the largest maximum eigenvalue. Finding this optimal submatrix is what renders the problem…
We introduce spiky rank, a new matrix parameter that enhances blocky rank by combining the combinatorial structure of the latter with linear-algebraic flexibility. A spiky matrix is block-structured with diagonal blocks that are arbitrary…
Considering the shortcomings of the traditional sample covariance matrix estimation, this paper proposes an improved global minimum variance portfolio model and named spectral corrected and regularized global minimum variance portfolio…
We describe a puzzle involving the interactions between an optimization of a multivariate quadratic function and a "plug-in" estimator of a spiked covariance matrix. When the largest eigenvalues (i.e., the spikes) diverge with the…
We show that when a high-dimensional data matrix is the sum of a low-rank matrix and a random error matrix with independent entries, the low-rank component can be consistently estimated by solving a convex minimization problem. We develop a…
We introduce a new criterion, the Rank Selection Criterion (RSC), for selecting the optimal reduced rank estimator of the coefficient matrix in multivariate response regression models. The corresponding RSC estimator minimizes the Frobenius…
We investigate the rank of random (symmetric) sparse matrices. Our main finding is that with high probability, any dependency that occurs in such a matrix is formed by a set of few rows that contains an overwhelming number of zeros. This…
Recent work has generalized several results concerning the well-understood spiked Wigner matrix model of a low-rank signal matrix corrupted by additive i.i.d. Gaussian noise to the inhomogeneous case, where the noise has a variance profile.…
Advances in modern technology have enabled the simultaneous recording of neural spiking activity, which statistically can be represented by a multivariate point process. We characterise the second order structure of this process via 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…
Given a known matrix that is the sum of a low rank matrix and a masked sparse matrix, we wish to recover both the low rank component and the sparse component. The sparse matrix is masked in the sense that a linear transformation has been…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate…
We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…
Evanescent random fields arise as a component of the 2-D Wold decomposition of homogenous random fields. Besides their theoretical importance, evanescent random fields have a number of practical applications, such as in modeling the…
We study the estimation of the covariance matrix $\Sigma$ of a $p$-dimensional normal random vector based on $n$ independent observations corrupted by additive noise. Only a general nonparametric assumption is imposed on the distribution of…
Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental problem in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Towards bridging…
Estimation of the covariance matrix of asset returns from high frequency data is complicated by asynchronous returns, market mi- crostructure noise and jumps. One technique for addressing both asynchronous returns and market microstructure…
In sparse principal component analysis we are given noisy observations of a low-rank matrix of dimension $n\times p$ and seek to reconstruct it under additional sparsity assumptions. In particular, we assume here each of the principal…
Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…